arXiv subjects

Wei-Qiang Chen

Publications and source records attributed to Wei-Qiang Chen.

At least 37 records · Page 2Linked to original sources

arXiv2024

$Z_{2}$ order fractionalization, topological phase transition, and odd frequency pairing in an exactly solvable spin-charge ladder

Motivated by the order fractionalization in Kitaev-Kondo model, we propose an exactly solvable spin-charge ladder model to study the order fractionalization with discrete symmetry. The spin-charge ladder is composed of a spin chain and a superconducting wire coupled via an Ising-type interaction, and we obtain the exact solution in the flat band limit. The exact solution reveals the $Z_{2}$ order fractionalization with dual symmetry breaking and intertwined order parameters. We investigate the topological phase transition of the spin-charge ladder via the spectral chiral index, and identify the correlated topological superconductor (TSC*) phase with gapped $Z_{2}$ Kondo flux excitations. We demonstrate Majorana spinons generated odd frequency pairing in the superconducting wire. We also discuss the order fractionalization in the perspective of $Z_{2}$ lattice gauge theory.

cond-mat.str-el↗

arXiv2024

On a class of fusion 2-category symmetry: condensation completion of braided fusion category

Recently, many studies are focused on generalized global symmetry, a mixture of both invertible and non-invertible symmetries in various space-time dimensions. The complete structure of generalized global symmetry is described by higher fusion category theory. In this paper, We first review the construction of fusion 2-category symmetry $Σ\cal B$ where $\cal B$ is a a braided fusion category. In particular, we elaborate on the monoidal structure of $Σ\cal B$ which determines fusion rules and controls the dynamics of topological operators/defects. We then take $Σ\mathrm{sVec}$ as an example to demonstrate how we calculate fusion rule, quantum dimension and 10j-symbol of the fusion 2-category. With our algorithm, all these data can be efficiently encoded and computed in computer program. The complete program will be uploaded to github soon. Our work can be thought as explicitly computing the representation theory of $\cal B$, in analogy to, for example the representation theory of $SU(2)$. The choice of basis bimodule maps are in analogy to the Clebsch-Gordon coefficients and the 10j-symbol are in analogy to the 6j-symbol.

hep-th↗

arXiv2023

The s$^\pm$-Wave Pairing and the Destructive Role of Apical-Oxygen Deficiencies in La$_3$Ni$_2$O$_7$ Under Pressure

Recently, the bilayer perovskite nickelate La$_3$Ni$_2$O$_7$ has been reported to show evidence of high-temperature superconductivity (SC) under a moderate pressure of about 14 GPa. To investigate the superconducting mechanism, pairing symmetry, and the role of apical-oxygen deficiencies in this material, we perform a random-phase-approximation based study on a bilayer model consisting of the $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals of Ni atoms in both the pristine crystal and the crystal with apical-oxygen deficiencies. Our analysis reveals an $s^{\pm}$-wave pairing symmetry driven by spin fluctuations. The crucial role of pressure lies in that it induces the emergence of the $γ$-pocket, which is involved in the strongest Fermi-surface nesting. We further found the emergence of local moments in the vicinity of apical-oxygen deficiencies, which significantly suppresses the $T_c$. Therefore, it is possible to significantly enhance the $T_c$ by eliminating oxygen deficiencies during the synthesis of the samples.

cond-mat.supr-con↗

arXiv2023

Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbor couplings $J_{1x}$, $J_{1y}$ and the next nearest neighbor coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence bond solid phase is observed.(Of course, the possibility of weakly first order transition can not be fully excluded.) With growing $J_{1y}/J_{1x}$, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM--VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL--VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

cond-mat.str-el↗

arXiv2023

Twofold Symmetry Observed in Bi$_{2}$Te$_{3}$/FeTe Interfacial Superconductor

Superconducting pairing symmetry are crucial in understanding the microscopic superconducting mechanism of a superconductor. Here we report the observation of a twofold superconducting gap symmetry in an interfacial superconductor Bi$_{2}$Te$_{3}$/FeTe, by employing quasiparticle interference (QPI) technique in scanning tunneling microscopy and macroscopic magnetoresistance measurements. The QPI patterns corresponding to energies inside and outside the gap reveal a clear anisotropic superconducting gap. Furthermore, both the in-plane angle-dependent magnetoresistance and in-plane upper critical field exhibit a clear twofold symmetry. This twofold symmetry align with the Te-Te direction in FeTe, which weakens the possible generation by bi-collinear antiferromagnetism order. Our finding provides key information in further understanding of the topological properties in Bi$_{2}$Te$_{3}$/FeTe superconducting system and propels further theoretical interests in the paring mechanism in the system.

cond-mat.supr-con↗

arXiv2023

Fate of entanglement in one-dimensional fermion liquid with coherent particle loss

Quantum many-body systems and quantum devices experience the detrimental effects of noise and particle losses, necessitating their treatment as open quantum systems or, in approximation, as non-Hermitian systems. These systems exhibit nontrivial characteristics in their time evolution that differ significantly from closed systems. In this Letter, we study the dynamic properties of a one-dimensional fermionic system with adjacent-lattice particle loss. By utilizing time-dependent correlation matrix methods and bosonization techniques, we demonstrate that, as the system evolves over time, its (bipartite) von Neumann entropy exhibits a universal behavior of rapid increase due to thermalization effects at short times, independent of the effective Hamiltonian and Liouvillian spectra, even in the presence of interactions. Additionally, we show that the asymmetric non-Hermitian terms in the effective Hamiltonian caused by adjacent-lattice quantum jumps lead to left-right asymmetry of quasiparticles in momentum space, which is ubiquitous in non-Hermitian skin effects and introduces momentum-space entanglement independent of the interaction strength at early times. Our study illuminates the universal fate of non-Hermitian fermionic liquids in the open quantum context, enriching our understanding of non-Hermitian many-body systems over the entire time range. Furthermore, our findings provide valuable insights for near-term quantum devices and the quantum simulation of open systems.

quant-ph↗

arXiv2023

Exceptional entanglement in non-Hermitian fermionic models

Exotic singular objects, known as exceptional points, are ubiquitous in non-Hermitian physics. They might be spectral singularities in energy bands that produce anomalous effects and defectiveness. The quantum entanglement of a generic non-Hermitian model with two different types of spectral exceptional points (SEPs) is systematically investigated in this paper. We discovered a relationship between non-unitary conformal field theories and the $k$-linear-type SEPs, which is typically associated with $\mathcal{PT}$-symmetry or pesdo-Hermicity spontaneous breaking. The underlying association between $k$-square-root-type SEPs, which arise concurrently with real (imaginary) gap closing in the complex spectrum, mimicking first-order-phase-transition criticalities, and complex conformal field theories (cCFTs) is addressed through the calculation of complex central charges. From the entanglement spectrum, zero-energy exceptional modes are found to be distinct from normal zero modes or topological boundary modes. Finally, we include a brief discussion of analogous non-Hermitian quantum spin models and endeavor to establish an intuitive understanding of exceptional points through the spin picture in various scenarios.

quant-ph↗

arXiv2023

Fate of Quantum Anomalies for 1d lattice chiral fermion with a simple non-Hermitian Hamiltonian

It is generally believed that the 1+1D model for a single chiral fermion does not exist by itself alone on lattice. The obstruction to such a lattice realization is the failure to reproduce the quantum anomalies of a chiral fermion in continuum. The conventional way to escape is to associate the anomalous 1d system with a 2d bulk, which is in a topologically non-trivial state, as the boundary of the latter. In this paper, we propose a 1+1D chiral fermion model on 1d spatial lattice, {standing alone} -- without being associated with a 2d bulk -- with a simple {non-Hermitian} hopping Hamiltonian. We demonstrate, using various methods, that the model possesses the same chiral anomaly and gravitational anomaly as in continuum theory. Furthermore, with appropriate parameters, the low energy effective theory of the model remains a field theory for unitary chiral fermions. The essential reason for the success is that the usual "doubled" fermion mode with opposite chirality is rapidly damped out because of non-Hermicity of the Hamiltonian.

cond-mat.other↗

arXiv2023

Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist

In this paper, we propose a general scheme to realize chiral TSCs through the "twistronics". Suppose we have a $D_n$-symmetric monolayer superconductor, which carries non-topological SC with pairing angular momentum $L=n/2$. Here we propose that we can obtain chiral TSC with the same $L$, by stacking two such monolayers with the largest twist angle $π/n$, forming a Moireless quasi-crystal (QC) structure, dubbed as the twist-bilayer QC (TB-QC) here. The chiral TSC in the TB-QC is driven by the interlay Josephson coupling between the pairing order parameters of the two layers. An argument based on the universal Ginzburg-Landau theory is provided to understand this proposal. One known example which fits our proposal is the $d+id$-chiral TSC in the 45$^\circ$-twisted bilayer cuprates. Here, based on the microscopic framework developed previously to treat with the electron-electron interactions in the TB-QC, we demonstrate the application of our proposal to a new example, i.e., the $f+if$-chiral TSC obtained by twisting two properly-doped honeycomb-Hubbard-model monolayers by the angle 30$^\circ$. This example is related to the newly synthesized 30$^\circ$-twisted bilayer graphene.

cond-mat.supr-con↗

arXiv2023

Spin-charge separation and unconventional superconductivity in \textit{t}-\textit{J} model on honeycomb lattice

The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or $t$-$J$ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the $d+id$-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t$-$J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of $t/J$, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed.

cond-mat.str-el↗

arXiv2022

Cooper instability and superconductivity on the Penrose lattice

Bulk superconductivity (SC) has recently been observed in the Al-Zn-Mg quasicrystal (QC). To settle several fundamental issues of the SC on the QC, we use an attractive Hubbard model to perform a systematic study on the Penrose lattice. The first issue is the Cooper instability of the QC, i.e., no Fermi surface under an infinitesimal attractive interaction. Starting from the two-electron problem outside the filled Fermi-sea, we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which provides the basis of the SC on the QC. Our numerical results yield that the Cooper pairing always takes place between the two time-reversal states, satisfying the Anderson's theorem. On this theorem, we perform a mean-field (MF) study at both zero and finite temperatures. The MF study also shows that an arbitrarily weak attraction can lead to the pairing order, with the resulted pairing state being well described by the BCS theory and the thermal dynamic behaviors being well consistent with experimental results. The second issue is about the superfluid density on the QC without translational symmetry. It's clarified that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits real SC, carrying finite superfluid density that can be verified by the Meissner effect, consistent with experiment also. These revealed properties of the SC on the Penrose lattice are universal for all QCs.

cond-mat.supr-con↗

arXiv2022

Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene

Starting from a realistic extended Hubbard model for a $p_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the MA-TBG near the van Hove (VH) dopings. Here we focus on the interplay between the approximate SU(2)$\times$SU(2) symmetry and the $D_3$ symmetry, which leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic RPA based calculations followed by a succeeding mean-field energy minimization for the ground state energy. At the SU(2)$\times$SU(2) symmetric point, the degenerate inter-valley SDW and VDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-valley DW. This state simultaneously hosts three 4-component vectorial spin-valley DW orders with each adopting one wave vector, and the polarization directions of the three DW orders are mutually perpendicular to one another. %in the $\mathbb{R}^4$ space. In the presence of a tiny inter-valley exchange interaction with coefficient $J_H\to 0^{-}$ which breaks the SU(2)$\times$SU(2) symmetry, a pure chiral SDW state is obtained. In the case of $J_H\to 0^{+}$, a nematic VDW+SDW state emerges which possesses a stripy distribution of the charge density, consistent with the recent STM observations. On the aspect of SC, while the triplet $p+ip$ and singlet $d+id$ topological SCs are degenerate at $J_H=0$ near the VH dopings, the former (latter) is favored for $J_H\to 0^{-}$ ($J_H\to 0^{+}$). In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments.

cond-mat.str-el↗

arXiv2022

High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

We study the largest-angle twisted homo-bilayer (LA-THB) systems, hosting Moiréless quasi-crystal (QC) structure. We propose to use these materials to generate high-angular-momentum (HAM) topological superconductivities (TSCs) protected by their QC symmetries absent on conventional crystalline materials. This proposal is based on our universal Ginzburg-Landau theory based analysis which yields the general conclusion that, when each $D_n$-symmetric ($n$ is even) monolayer hosts SC with pairing angular momentum $l\le \frac{n}{2}$, the interlayer Josephson coupling will induce SC with pairing angular momentum $L=l$ or $L=n-l$ in the LA-THB, determined by microscopic details. The latter one is just the HAM TSC if $l>0$. Based on our revised perturbational-band theory, we develop general microscopic framework to study the QC LA-THBs involving electron-electron interactions, adopting which we study three examples, i.e. the 30$^\circ$- twisted bilayer graphene, the 30$^\circ$- twisted bilayer BC$_3$, and the 45$^\circ$- twisted bilayer cuprates. The $g+ig$- $h+ih$- and $d+id$- TSCs with HAM $L=4,5$ and $2$ can emerge in certain doping regimes in these systems, respectively.

cond-mat.supr-con↗

arXiv2021

The emergence of gapless quantum spin liquid from deconfined quantum critical point

A quantum spin liquid (QSL) is a novel phase of matter with long-range entanglement where localized spins are highly correlated with the vanishing of magnetic order. Such exotic quantum states provide the opportunities to develop new theoretical frameworks for many-body physics and have the potential application in realizing robust quantum computations. Here we show that a gapless QSL can naturally emerge from a deconfined quantum critical point (DQCP), which is originally proposed to describe Landau forbidden continuous phase transition between antiferromagnetic (AFM) and valence-bond solid (VBS) phases. Via large-scale tensor network simulations of a square-lattice spin-1/2 frustrated Heisenberg model, both QSL state and DQCP-type AFM-VBS transition are observed. With tuning coupling constants, the AFM-VBS transition vanishes and instead, a gapless QSL phase gradually develops in between. Remarkably, along the phase boundaries of AFM-QSL and QSL-VBS transitions, we always observe the same correlation length exponents $ν\approx 1.0$, which is intrinsically different from the one of the DQCP-type transition, indicating new types of universality classes. Our results explicitly demonstrate a new scenario for understanding the emergence of gapless QSL from an underlying DQCP. The discovered QSL phase survives in a large region of tuning parameters and we expect its experimental realizations in solid state materials or quantum simulators.

cond-mat.str-el↗

arXiv2021

A lattice realization of general three-dimensional topological order

Topological orders are a class of phases of matter that beyond the Landau symmetry breaking paradigm. The two (spatial) dimensional (2d) topological orders have been thoroughly studied. It is known that they can be fully classified by a unitary modular tensor category (UMTC) and a chiral central charge c. And a class of 2d topological orders whose boundary are gappable can be systematically constructed by Levin-Wen model whose ground states are string-net condensed states. Previously, the three spatial dimensional topological orders have been classified based on their canonical boundary described by some special unitary fusion 2-category, $2\mathcal{V}ec_G^ω$ or an EF 2-category. However, a lattice realization of a three spatial dimensional topological orders with both canonical boundary and arbitrary boundaries are still lacking. In this paper, we construct a 3d membrane-net model based on spherical fusion 2-category, which can be used to systematically study all general 3d topological order with gapped boundary. The partition function and lattice Hamiltonian of the membrane-net model is constructed based on state sum of spherical fusion 2-category. We also construct the 3d tube algebra of the membrane-net model to study excitations in the model. We conjecture all intrinsic excitations in membrane-net model have a one-to-one correspondence with the irreducible central idempotents (ICI) of the 3d tube algebra. We also provide a universal framework to study mutual statistics of all excitations in 3d topological order through 3d tube algebra. Our approach can be straightforwardly generalized to arbitrary dimension.

cond-mat.str-el↗

arXiv2021

Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model

The nature of the zero-temperature phase diagram of the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice has been debated in the past three decades, which may hold the key to understand high temperature superconductivity. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram the $J_1$-$J_2$ Heisenberg model up to $24\times 24$ sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56\lesssim J_2/J_1\leq0.61$ before the system enters the well known collinear antiferromagnetic phase. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for precisely capturing long-range physcis for highly frustrated systems, and also demonstrate the finite PEPS method is a very powerful approach to study strongly corrleated quantum many-body problems.

cond-mat.str-el↗

arXiv2021

$g+ig$ topological superconductivity in the 30$^o$-twisted bilayer graphene

Based on our revised perturbational-band theory, we study possible pairing states driven by interaction in the electron-doped quasicrystal 30\degree-twisted bilayer graphene. Our mean-field study on the related t-J model predicts that, the beneath-van-Hove and beyond-van-Hove low doping regimes are covered by the chiral $d+id$ and $g+ig$ topological superconductivities (TSCs) respectively. The $g+ig$-TSC possesses a pairing angular momentum 4, and hence following each effective $C_{12}$- rotation by $Δϕ=nπ/6$, the pairing phase changes $4Δϕ$. This intriguing TSC is novel, as it belongs to a special 2D $E_4$- irreducible representation of the effective $D_{12}$ point group unique to this quasicystal and absent on periodic lattices. The Ginzburg-Landau theory suggested that the $g+ig$- TSC originates from the Josephson coupling between the $d+id$ pairings on the two mono-layers.

cond-mat.str-el↗

arXiv2021

Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

cond-mat.str-el↗