# X. Wen

## Contact Details

NameX. Wen |
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## Pubs By Year |
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## Pub CategoriesPhysics - Strongly Correlated Electrons (26) High Energy Physics - Theory (11) Quantum Physics (8) Mathematics - Mathematical Physics (7) Mathematical Physics (7) Physics - Mesoscopic Systems and Quantum Hall Effect (5) Physics - Optics (4) Nonlinear Sciences - Pattern Formation and Solitons (4) Instrumentation and Methods for Astrophysics (4) Physics - Instrumentation and Detectors (4) Nonlinear Sciences - Exactly Solvable and Integrable Systems (4) Physics - Statistical Mechanics (3) High Energy Physics - Phenomenology (3) Mathematics - Quantum Algebra (3) Mathematics - Category Theory (3) Nuclear Experiment (2) Mathematics - Analysis of PDEs (2) Physics - Other (1) Mathematics - Information Theory (1) Computer Science - Information Theory (1) Mathematics - Geometric Topology (1) Physics - Classical Physics (1) Mathematics - Optimization and Control (1) Physics - Physics and Society (1) |

## Publications Authored By X. Wen

**Authors:**H. L. Xiao, W. Hajdas, P. Socha, R. Marcinkowski, B. B. Wu, T. W. Bao, J. Y. Chai, Y. W. Dong, M. N. Kong, L. Li, Z. H. Li, J. T. Liu, H. L. Shi, L. M. Song, J. C. Sun, R. J. Wang, Y. H. Wang, X. Wen, S. L. Xiong, J. Zhang, L. Y. Zhang, S. N. Zhang, X. F. Zhang, Y. J. Zhang, F. Cadoux, M. Pohl, X. Wu, T. Batsch, D. Rybka, A. Rutczynska, J. Szabelski, A. Zwolinska, N. Gauvin, N. Produit, T. Bernasconi

POLAR is space-borne detector designed for a precise measurement of gamma-ray polarization of the prompt emissions of Gamma-Ray Bursts in the energy range 50 keV - 500 keV. POLAR is a compact Compton polarimeter consisting of 40$\times$ 40 plastic scintillator bars read out by 25 multi-anode PMTs. In May 2015, we performed a series of tests of the POLAR flight model with 100\% polarized x-rays beams at the European Synchrotron Radiation Facility beam-line ID11 aming to study thresholds, crosstalk between channels and responses of POLAR flight model to polarized X-ray beams. Read More

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. Read More

A 2.8 dB polarization squeezing of Stokes operator S2 at rubidium D1 line (795nm) is achieved, and the lowest squeezing band reached the audio frequency at 2.6 kHz. Read More

The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. Read More

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrodinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc. Read More

**Authors:**X. F. Zhang, W. Hajdas, H. L. Xiao, X. Wen, B. B. Wu, T. W. Bao, T. Batsch, T. Bernasconi, F. Cadoux, I. Cernuda, J. Y. Chai, Y. W. Dong, N. Gauvin, J. J. He, M. Kole, M. N. Kong, C. Lechanoine-Leluc, L. Li, Z. H. Li, J. T. Liu, X. Liu, R. Marcinkowski, S. Orsi, M. Pohl, D. Rapin, D. Rybka, H. L. Shi, L. M. Song, J. C. Sun, J. Szabelski, R. J. Wang, Y. H. Wang, X. Wu, S. L. Xiong, M. Xu, L. Zhang, L. Y. Zhang, P. Zhang, S. N. Zhang, Y. J. Zhang, A. Zwolinska

As a space-borne detector POLAR is designed to conduct hard X-ray polarization measurements of gamma-ray bursts on the statistically significant sample of events and with an unprecedented accuracy. During its development phase a number of tests, calibrations runs and verification measurements were carried out in order to validate instrument functionality and optimize operational parameters. In this article we present results on gain optimization togeter with verification data obtained in the course of broad laboratory and environmental tests. Read More

In this paper, we study the relation between an anomaly-free $n+$1D topological order, which are often called $n+$1D topological order in physics literature, and its $n$D gapped boundary phases. We argue that the $n+$1D bulk anomaly-free topological order for a given $n$D gapped boundary phase is unique. This uniqueness defines the notion of the "bulk" for a given gapped boundary phase. Read More

We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one. We show that such construction is reversible and leads to a new equivalence relation between topological orders. We refer to the corresponding equivalent class (the orbit of the hierarchy construction) as "the non-Abelian family". Read More

The Letter reports an experimental observation of the classical version of valley polarized states in a two-dimensional hexagonal sonic crystal, where the inversion-symmetry breaking of scatterers induces an omnidirectional frequency gap. The acoustic valley states, which carry specific linear momenta and orbital angular momenta, were selectively excited by external Gaussian beams and conveniently confirmed by the pressure distribution outside the crystal, according to the criterion of momentum conservation. The vortex nature of such intriguing crystal states was directly characterized by scanning the phase profile inside the crystal. Read More

**Authors:**M. Kole, T. W. Bao, T. Batsch, T. Bernasconi, F. Cadoux, J. Y. Chai, Y. W. Dong, N. Gauvin, W. Hajdas, J. J. He, M. N. Kong, S. W. Kong, C. Lechanoine-Leluc, L. Li, Z. H. Li, J. T. Liu, X. Liu, R. Marcinkowski, S. Orsi, M. Pohl, N. Produit, D. Rapin, A. Rutczynska, D. Rybka, H. L. Shi, L. M. Song, J. C. Sun, J. Szabelski, R. J. Wang, Y. J. Wang, X. Wen, B. B. Wu, X. Wu, H. L. Xiao, S. L. Xiong, H. H. Xu, M. Xu, J. Zhang, L. Zhang, L. Y. Zhang, S. N. Zhang, X. F. Zhang, Y. J. Zhang, A. Zwolinska

Gamma-ray polarimetry is a new powerful tool to study the processes responsible for the emission from astrophysical sources and the environments in which this emission takes place. Few successful polarimetric measurements have however been performed thus far in the gamma-ray energy band due to the difficulties involved. POLAR is a dedicated polarimeter designed to perform high precision measurements of the polarization of the emission from gamma-ray burst in the 50-500 keV energy range. Read More

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a 3+1D $Z_2$ gauge theory with emergent fermionic Kramer doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin$^+$ structure. Read More

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1, N-1)-fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Read More

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Read More

Entanglement evolutions after a global quantum quench and a local quantum quench in 1+1 dimensional conformal field theories (CFTs) show qualitatively different behaviors, and are studied within two different setups. In this work, we bridge global and local quantum quenches in (1+1)-d CFTs in the same setup, by studying the entanglement evolution from a specific inhomogeneous initial state. By utilizing conformal mappings, this inhomogeneous quantum quench is analytically solvable. Read More

This paper combines and develops the models in Lastrapes (2002) and Mankiw & Weil (1989), which enables us to analyze the effects of interest rate and population growth shocks on housing price in one integrated framework. Based on this model, we carry out policy simulations to examine whether the housing (stock or flow) tax reduces the housing price fluctuations caused by interest rate or population growth shocks. Simulation results imply that the choice of housing tax tools depends on the kind of shock that housing market faces. Read More

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature. Read More

In an improved multisource thermal model, we systematically investigate the transverse momentum spectra in pp collisions at high energies ranging from 62.4 GeV to 7 TeV. The results are compared with the experimental data in RHIC and LHC. Read More

Integrated optical power splitter is one of the fundamental building blocks in photonic integrated circuits (PIC). Conventional multimode interferometer based power splitter is widely used as it has reasonable footprint and is easy to fabricate. However, it is challenging to realize arbitrary split ratio especially for multi-outputs. Read More

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. Read More

The occupied Landau levels of strange quark matter are investigated in the framework of the SU(3) NJL model with a conventional coupling and a magnetic-field dependent coupling respectively. At lower density, the Landau levels are mainly dominated by u and d quarks. Threshold values of the chemical potential for the s quark onset are shown in the $\mu$-$B$ plane. Read More

Underwater sound isolation has been a long-standing fundamental issue in industry and military fields. Starting from a simple theoretical model, here an air-sealed metasurface is proposed to overcome this problem. Comparing with the sample without filling air, the effective impedance of the air-sealed one is greatly reduced and strikingly mismatch with water, accompanying another merit of low sound speed. Read More

We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Read More

We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Read More

In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. Read More

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density of the CFT, and $f(x)$ is an envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian, and the so-called sine-square deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Read More

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g. Read More

To avoid simultaneous charging and discharging of storages, complementarity constraints are introduced to storage-concerned economic dispatch (ED), which makes the problem non-convex. This letter concerns the conditions under which the convex relaxation of storage-concerned ED with complementarity constraints is exact. Two new sufficient conditions are proposed, proved and verified to significantly reduce the conservatism of recent results [3], [4]. Read More

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are classified, up to $E_8$ quantum Hall states, by the unitary modular tensor categories $\mathcal{C}$ over $\mathcal{E}$ and the modular extensions of each $\mathcal{C}$. In the case $\mathcal{C}=\mathcal{E}$, we prove that the set $\mathcal{M}_{ext}(\mathcal{E})$ of all modular extensions of $\mathcal{E}$ has a natural structure of a finite abelian group. Read More

Gapped quantum liquids (GQL) include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQL for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by non-degenerate unitary braided fusion categories over a symmetric fusion category (SFC) $\cal E$, abbreviated as $\text{UMTC}_{/\cal E}$, together with their modular extensions and total chiral central charges. The SFC $\cal E$ is $\text{Rep}(G)$ for bosonic symmetry $G$, or $\text{sRep}(G^f)$ for fermionic symmetry $G^f$. Read More

We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped states of matter with intrinsic topological orders. Second, we introduce the braiding statistics data of particles and strings, such as the geometric Berry matrices for particle-string Aharonov-Bohm and multi-loop adiabatic braiding process, encoded by submanifold linkings, in the closed spacetime 3-manifolds and 4-manifolds. Read More

One of the most important problems in complex networks is how to detect metadata groups accurately. The main challenge lies in the fact that traditional structural communities do not always capture the intrinsic features of metadata groups. Motivated by the observation that metadata groups in PPI networks tend to consist of an abundance of interacting triad motifs, we define a 2-club substructure with diameter 2 which possessing triad-rich property to describe a metadata group. Read More

It was recently derived that the QCD running coupling is a function of the magnetic field strength under the strong magnetic field approximation. Inspired by this progress and based on the self-consistent solutions of gap equations, the properties of two-flavor and three-flavor quark matter are studied in the framework of the Nambu-Jona-Lasinio model with a magnetic-field dependent running coupling. We find that the dynamical quark masses as functions of the magnetic field strength are not monotonous in the fully chirally broken phase. Read More

A continuous-wave Ti:sapphire laser at 795 nm is frequency doubled in a bow-tie type enhancement four-mirror ring cavity with LiB3O5 (LBO), BiB3O6 (BiBO), and periodically polled KTiOPO4 (PPKTP) crystals, respectively. The properties of 397.5 nm ultra-violet (UV) output power, beam quality, stability for these different nonlinear crystals are investigated and compared. Read More

In this paper, we calculate the entanglement negativity in free-fermion systems by use of the overlap matrices. For a tripartite system, if the ground state can be factored into triples of modes, we show that the partially transposed reduced density matrix can be factorized and the entanglement negativity has a simple form. However, the factorability of the ground state in a tripartite system does not hold in general. Read More

We report on efficient generation of second harmonic laser and single-mode vacuum squeezed light of 795 nm with periodically poled KTiOPO4 (PPKTP) crystals. We achieved 111 mW of ultra-violet (UV) light at 397.5 nm from 191 mW of fundamental light with a PPKTP crystal in a doubling cavity, corresponding to a conversion efficiency of 58. Read More

A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry protected topological (SPT) phases in 2+1 dimensional space-time by using this charged entanglement entropy. SPT phases are short range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. Read More

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. Read More

**Authors:**H. L. Xiao, W. Hajdas, T. W. Bao, T. Batsch, T. Bernasconi, I. Cernuda, J. Y. Chai, Y. W. Dong, N. Gauvin, M. Kole, M. N. Kong, S. W. Kong, L. Li, J. T. Liu, X. Liu, R. Marcinkowski, S. Orsi, M. Pohl, N. Produit, D. Rapin, A. Rutczynska, D. Rybka, H. L. Shi, L. M. Song, J. C. Sun, J. Szabelski, B. B. Wu, R. J. Wang, X. Wen, H. H. Xu, L. Zhang, L. Y. Zhang, S. N. Zhang, X. F. Zhang, Y. J. Zhang, A. Zwolinska

Gamma Ray Bursts (GRBs) are the strongest explosions in the universe which might be associated with creation of black holes. Magnetic field structure and burst dynamics may influence polarization of the emitted gamma-rays. Precise polarization detection can be an ultimate tool to unveil the true GRB mechanism. Read More

This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. Read More

Self-consistent (non-)abelian statistics in 2+1D are classified by modular tensor categories (MTC). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients $N^{ij}_k$ and spins $s_i$, was proposed. A numerical search based on these axioms led to a list of possible (non-)abelian statistics, with rank up to $N=7$. Read More

**Authors:**Hualin Xiao, Wojtek Hajdas, Bobing Wu, Nicolas Produit, Tianwei Bao, Tadeusz Batsch, Ilia Britvich, Franck Cadoux, Junying Chai, Yongwei Dong, Neal Gauvin, Minnan Kong, Siwei Kong, Dominik K. Rybka, Catherine Leluc, Lu Li, Jiangtao Liu, Xin Liu, Radoslaw Marcinkowski, Mercedes Paniccia, Martin Pohl, Divic Rapin, Aleksandra Rutczynska, Haoli Shi, Liming Song, Jianchao Sun, Jacek Szabelski, Ruijie Wang, Xing Wen, Hanhui Xu, Laiyu Zhang, Li Zhang, Shuangnan Zhang, Xiaofeng Zhang, Yongjie Zhang, Ania Zwolinska

In spite of extensive observations and numerous theoretical studies in the past decades several key questions related with Gamma-Ray Bursts (GRB) emission mechanisms are still to be answered. Precise detection of the GRB polarization carried out by dedicated instruments can provide new data and be an ultimate tool to unveil their real nature. A novel space-borne Compton polarimeter POLAR onboard the Chinese space station TG2 is designed to measure linear polarization of gamma-rays arriving from GRB prompt emissions. Read More

We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC describes a fermionic product state without symmetry or a fermionic/bosonic product state with symmetry $G$, and the UBFC has a modular extension. We developed a simplified theory of non-degenerate UBFC over a SFC based on the fusion coefficients $N^{ij}_k$ and spins $s_i$. This allows us to obtain a list that contains all 2+1D fermionic topological orders (without symmetry). Read More

Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor $S(\mathbf{q},\omega)$ of spin liquid states on the kagome lattice. Spin-1 excited states in spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). Read More

In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. Read More

**Authors:**Ming Gong, Xueda Wen, Guozhu Sun, Dan-Wei Zhang, Dong Lan, Yu Zhou, Yunyi Fan, Yuhao Liu, Xinsheng Tan, Haifeng Yu, Yang Yu, Shi-Liang Zhu, Siyuan Han, Peiheng Wu

The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. Read More

**Authors:**Guozhu Sun, Jiquan Zhai, Xueda Wen, Yang Yu, Lin Kang, Weiwei Xu, Jian Chen, Peiheng Wu, Siyuan Han

We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Read More

Spontaneous symmetry breaking is well understood through the classical "Mexican Hat" picture, which describes many quantum phases of matter. Recently, several new classes of quantum phases of matter, such as topological orders and symmetry protected topological (SPT) orders, were discovered. In an attempt to address the transitions between all those phases of quantum matter under the same framework, we introduced an analogous yet very simple picture for phase transitions in the context of tensor-networks. Read More

Quantum-disordering a discrete-symmetry breaking state by condensing domain-walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a 1D representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain-walls can lead to a non-trivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a non-trivial SPT invariant -- the symmetry-twist dependent partition function. Read More

In this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints. We combine beamforming with full-rate high dimensional real-valued orthogonal space time block coding (OSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design. The original multi-constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation (SDR) which can be solved efficiently. Read More

In this paper, we study the relation between topological orders and their gapped boundaries. We propose that the bulk for a given gapped boundary theory is unique. It is actually a consequence of a microscopic definition of a local topological order, which is a (potentially anomalous) topological order defined on an open disk. Read More