arXiv subjects

Su-Peng Kou

Publications and source records attributed to Su-Peng Kou.

At least 37 records · Page 2Linked to original sources

arXiv2023

Aufbau Principle for Non-Hermitian Systems

We develop a generalized Aufbau principle for non-Hermitian systems that allows for building up the configurations of indistinguishable particles. The Aufbau rule of non-Hermitian systems is unexpectedly shown to be identical to that developed in Hermitian systems when the real parts of the complex energy levels are considered. We derive full many-body energy spectra of the fermionic and bosonic Hatano-Nelson models as examples by filling single-particle energy levels in the momentum space. For open boundary conditions, we show that many-body non-Hermitian skin effects persist in all many-body eigenstates for both fermions and bosons. Furthermore, we find surprisingly that the ground state of bosons is an anomalous Bose-Einstein condensation with all of the particles simultaneously localizing in both the real and momentum space beyond the Heisenberg uncertainty principle. For periodic boundary conditions, we show that hard-core bosons cannot be mapped to fermions. This work establishes a general framework for understanding the many-body physics of non-Hermitian systems, revealing rich unique non-Hermitian many-body physics.

quant-ph↗

arXiv2023

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

cond-mat.str-el↗

arXiv2023

Dynamical scaling of Loschmidt echo in non-Hermitian systems

We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.

cond-mat.str-el↗

arXiv2023

Symmetry classes of dissipative topological insulators with edge dark state

We classify the dissipative topological insulators (TIs) with edge dark states (EDS) by using the 38-fold way of non-Hermitian systems in this paper. The dissipative dynamics of these quadratic open fermionic systems is captured by a non-Hermitian single-particle matrix which contains both the internal dynamics and the dissipation, refereed to as damping matrix $X$. And the dark states in these systems are the eigenmodes of $X$ which the eigenvalues' imaginary part vanishes. However, there is a constraint on $X$, namely that the modes in which the eigenvalues' imaginary parts are positive are forbidden. In other words, the imaginary line-gap of $X$ is ill-defined, so the topological band theory classifying the dark states can not be applied to $X$. To reveal the topological protection of EDS, we propose the double damping matrix $\tilde{X} = \text{diag}\left( X, X^* \right)$, where the imaginary line-gap is well defined. Thus, the 38-fold way can be applied to $\tilde{X}$, and the topological protection of the EDS is uncovered. Different from previous studies of EDS in purely dissipative dynamics, the EDS in the dissipative TIs are robust against the inclusion of Hamiltonians. Furthermore, the topological classification of $\tilde{X}$ not only reflects the topological protection of EDS in dissipative TIs but also provides a paradigm to predict the appearance of EDS in other open free fermionic systems.

cond-mat.mes-hall↗

arXiv2021

Physics of PT-Symmetric Quantum Systems at Finite Temperature

We study parity-time-symmetric non-Hermitian quantum systems at finite temperature, where the Boltzmann distribution law fails to hold. To characterize their abnormal physical properties, a new quantum statistics theory (the so-called quantum Liouvillian statistics theory) was developed, in which the Boltzmann distribution law was replaced by the Liouvillian-Boltzmann distribution law. Using it, we derived analytical results of thermodynamic properties for thermal PT systems and found that a "continuous" thermodynamic phase transition occurs at the exceptional point, where a zero-temperature anomaly exists.

cond-mat.stat-mech↗

arXiv2021

Defective Majorana zero modes in non-Hermitian Kitaev chain

Topological stability is an important property for topological materials. However, the non-Hermitian effects may change this situation. Here, we investigate the robustness of edge states in the non-Hermitian Kitaev chain with imbalanced tunneling term and superconducting pairing term. By defining the similarity of Majorana zero modes (MZMs) and magnetic factor, the coalescing phase diagram of the MZMs and corresponding spin polarization phase diagram are provided. Because of the non-Hermitian coalescence effect and non-Hermitian suppression effect induced by the breakdown of sublattice symmetry and particle-hole symmetry, the system emergence very interesting phenomenons, such as defective MZMs, number-anomalous bulk-boundary correspondence, coalescing of many-body ground states, the magnetic phase crossover without gap closing. Those novel non-Hermitian effects offer fresh insights into MZMs and topological physics.

cond-mat.supr-con↗

arXiv2021

Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes

In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Majorana Fermions) is very important, really exotic, and completely robust. The race for searching Majorana zero modes and verifying the corresponding non-Abelian statistics becomes an important frontier in condensed matter physics. In this letter, we generalize the Majorana zero modes to non-Hermitian (NH) topological systems that show universal but quite different properties from their Hermitian counterparts. Based on the NH Majorana zero modes, the orthogonal and nonlocal Majorana qubits are well defined. In particular, due to the particle-hole-symmetry breaking, NH Majorana zero modes have irrational non-Abelian statistics with continuously tunable braiding Berry phase from pi/8 to 3pi/8. This is quite different from the usual non-Abelian statistics with fixed braiding Berry phase pi/4 and becomes an example of "irrational topological phenomenon". The one-dimensional NH Kitaev model is taken as an example to numerically verify the irrational non-Abelian statistics for two NH Majorana zero modes. The numerical results are exactly consistent with the theoretical prediction. With the help of braiding these two zero modes, the pi/8 gate can be reached and thus universal topological quantum computation becomes possible.

cond-mat.mes-hall↗

arXiv2020

Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry

Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.

cond-mat.str-el↗

arXiv2020

Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions

Unconventional lattice fermions with high degeneracies beyond Weyl and Dirac fermions have attracted intensive attention in recent years. In this paper, attention is drawn to the pseudospin-1 Maxwell fermions and the $(2+1)$ dimensional parity anomaly, which goes beyond the scope of "fermion doubling theorem". We have derived the Hall conductivity of a single Maxwell fermion, and showcased each Maxwell fermion contributes a quantized Hall conductance $e^{2}/h$. We observe that the parity is spontaneously broken in the effective theory of lattice Maxwell fermions interacting with an (auxiliary) $U(1)$ gauge field, leading to an effective anomaly-induced Chern-Simons theory. An interesting observation from the parity anomaly is that the lattice Maxwell fermions beyond the "fermion doubling theorem", so there exists single Maxwell fermion in a lattice model. In addition, our work indicates the quantum anomaly in odd-dimensional spinor space.

cond-mat.str-el↗

arXiv2020

Critical behavior of QED$_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge

The chiral QED$_3$--Gross-Neveu-Yukawa (QED$_3$-GNY) theory is a $2+1$-dimensional U(1) gauge theory with $N_f$ flavors of four-component Dirac fermions coupled to a scalar field. For $N_f=1$, the specific chiral Ising QED$_3$-GNY model has recently been conjectured to be dual to the deconfined quantum critical point that describes Neel--valence-bond-solid transition of frustrated quantum magnets on square lattice. We study the universal critical behaviors of the chiral QED$_3$-GNY model in $d=4-ε$ dimensions for an arbitrary $N_f$ . We calculate the boson anomalous dimensions, inverse correlation length exponent, as well as the scaling dimensions of nonsinglet fermion bilinear in the chiral QED$_3$-GNY model. The Pad$\acute{e}$ estimates for the exponents are obtained in the chiral Ising-, XY- and Heisenberg-QED$_3$-GNY universality class respectively. We also establish the general condition of the supersymmetric criticality for the ungauged QED$_3$-GNY model. For the conjectured duality between chiral QED$_3$-GNY critical point and deconfined quantum critical point, we find the inverse correlation length exponent has a lower boundary $ν^{-1}>0.75$, beyond which the Ising-QED$_3$-GNY--$\mathbb{C}$P$^1$ duality may hold.

cond-mat.str-el↗

arXiv2020

State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems

The breakdown of the bulk-boundary correspondence in non-Hermitian (NH) topological systems is an open, controversial issue. In this paper, to resolve this issue, we ask the following question: Can a (global) topological invariant completely describe the topological properties of a NH system as its Hermitian counterpart? Our answer is no. One cannot use a global topological invariant (including non-Bloch topological invariant) to accurately characterize the topological properties of the NH systems. Instead, there exist a new type of topological invariants that are absence in its Hermitian counterpart -- the state dependent topological invariants. With the help of the state-dependent topological invariants, we develop a new topological theory for NH topological system beyond the general knowledge for usual Hermitian systems and obtain an exact formulation of the bulk-boundary correspondence, including state-dependent phase diagram, state-dependent phase transition and anomalous transport properties (spontaneous topological current). Therefore, these results will help people to understand the exotic topological properties of various non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2020

Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation

It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su-SchriefferHeeger model and two-dimensional (deformed) Qi-Wu-Zhang model as examples, we focus on a special type of non-Hermitian topological system without non-Hermitian skin effect-topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, we introduce a new type of inversion symmetry-protected topological invariant-total Z2 topological invariant. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, we find that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to nonHermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

cond-mat.mes-hall↗

arXiv2020

Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{RT}$ symmetry

In this paper, based on a one-dimensional non-Hermitian spin model with $\mathcal{RT}$-invariant term, we study the non-Hermitian physics for the two (nearly) degenerate ground states. By using the high-order perturbation method, an effective pseudo-spin model is obtained to describe non-Hermitian physics for the two (nearly) degenerate ground states, which are precisely consistent with the numerical calculations. We found that there may exist effective (anti) $\mathcal{PT}$ symmetry for the effective pseudo-spin model of the two (nearly) degenerate ground states. In particular, there exists spontaneous (anti) $\mathcal{PT}$ -symmetry breaking for the topological degenerate ground states with tunable parameters in external fields. We also found that even a very tiny imaginary external field applied will drive $\mathcal{PT}$ phase transition.

cond-mat.stat-mech↗

arXiv2020

Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order

In this paper, based on a non-Hermitian toric-code model, we surprisingly find that the degeneracy of ground states can be changed by a local non-Hermitian perturbation (even in thermodynamic limit). We call it non-Hermitian avalanche effect. As the physics consequences of the non-Hermitian avalanche effect, a correspondence between bulk quasi-particles and topologically protected degenerate ground states for Z2 topological order is borken down. In addition, the PT symmetry breaking transition of the topologically degenerate ground states subspace can be observed by fidelity susceptibility.

cond-mat.mes-hall↗

arXiv2019

Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry

In this paper, with the help of Hermitian/non-Hermitian dynamic strings, the theory of non-Hermitian topological order is developed based on a non-Hermitian Wen-plaquette model. The effective models for bosonic topological excitations (e-particle and m-particle) are Hermitian tight-binding lattice model; the effective model for fermionic topological excitation (f-particle) becomes a non-Hermitian tight-binding lattice model. In addition, the effective pseudo-spin model for topologically degenerate ground states is derived by calculating the expectation values of Hermitian/non-Hermitian topological closed dynamic strings. For the topologically degenerate ground states of non-Hermitian Wen-plaquette model on an even-by-odd, odd-by-even and odd-by-odd lattice, anomalous topological degeneracy occurs, i.e., the number of the topologically protected ground states may be reduced from 2 to 1. Now, the effective pseudo-spin model turns into the typical PT-symmetric non-Hermitian Hamiltonian with spontaneous PT-symmetry breaking. At exceptional points, the topologically degenerate ground states merge with each other and the topological degeneracy turns into non-Hermitian degeneracy. In the end, the application of the non-Hermitian Z2 topological order and its possible physics realization are discussed.

cond-mat.mes-hall↗

arXiv2019

Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems

Non-Hermitian topological systems show quite different properties as their Hermitian counterparts. An important, puzzled issue on non-Hermitian topological systems is the existence of defective edge states beyond usual bulk-boundary correspondence (BBC) that localize either on the left edge or the right edge of the one-dimensional system. In this paper, to understand the existence of the defective edge states, the theory of anomalous bulk-boundary correspondence (A-BBC) is developed that distinguishes the non-Bloch bulk-boundary correspondence (NB-BBC) from non-Hermitian skin effect. By using the one-dimensional non-Hermitian Su-Schrieffer-Heeger model as an example, the underlying physics of defective edge states is explored. The defective edge states are physics consequence of boundary exceptional points of anomalous edge Hamiltonian. In addition, with the help of a theorem, the number anomaly of the edge states in non-Hermitian topological systems become a mathematic problem under quantitative calculations by identifying the Abelian/non-Abelian non-Hermitian condition for edge Hamiltonian and verifying the deviation of the BBC ratio from 1. In the future, the theory for A-BBC can be generalized to higher dimensional non-Hermitian topological systems (for example, 2D Chern insulator).

cond-mat.str-el↗

arXiv2019

It from Knot

Knot physics is the theory of the universe that not only unified all the fundamental interactions but also explores the underlying physics of quantum mechanics. In knot physics, the most important physical result is the unification of everything (including matter, motion, interaction and space-time, ...) into the entangled vortex-membranes (a knot): our universe is a projection of a four three dimensional entangled vortex-membranes in five dimensional inviscid incompressible fluid, of which the low energy effective theory not only reproduces the Standard model -- an SU_{strong}(3)}*SU_{weak}(2)*U_{Y}(1) gauge theory but also leads to the physics of general relativity. In a word, it from knot.

physics.gen-ph↗

arXiv2019

Fidelity as a probe for a deconfined quantum critical point

Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.

cond-mat.str-el↗