arXiv subjects

Li-Jun Lang

Publications and source records attributed to Li-Jun Lang.

At least 19 recordsLinked to original sources

arXiv2026

Fate of moir\'e flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional $\mathcal{PT}$-symmetric bichromatic optical lattices

One-dimensional (1D) superlattices provide one simplified platform for exploring moir\'e physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here, we propose a 1D $\mathcal{PT}$-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moir\'e flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the $\mathcal{PT}$-symmetric imaginary potential due to the distinct $\mathcal{PT}$ pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the $\mathcal{PT}$-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the $\mathcal{PT}$-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moir\'e bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moir\'e systems.

cond-mat.quant-gas↗

arXiv2026

Emergent Macroscopic Nonreciprocity from Identical Active Particles via Spontaneous Symmetry Breaking

Nonreciprocity is known to generate a wide range of exotic phenomena in multi-species many-body systems, where different species influence one another through couplings that violate Newton's third law. In contrast, in the absence of explicitly imposed macroscopic nonreciprocal processes, single-species nonreciprocity -- another distinct form of nonreciprocity -- typically plays only a limited role in shaping macroscopic physics. Here, using a single-species Vicsek model with a vision cone and extrinsic noise, we show that spontaneous symmetry breaking (SSB) can dramatically enhance the macroscopic consequences of microscopic single-species nonreciprocity. In the ordered phase, this enhancement gives rise to an emergent macroscopic nonreciprocity that induces the system of identical active particles to admit an effective description with a "two-species" non-Hermitian structure. The resulting SSB-enhanced nonreciprocity substantially promotes traveling-band formation and, more strikingly, drives a novel real-space condensation of identical active particles, characterized by a "traveling line" with vanishing longitudinal width. Our findings uncover a fundamental mechanism by which microscopic single-species nonreciprocity can exert strong macroscopic influences in complex systems.

cond-mat.stat-mech↗

arXiv2025

Electric circuit analog of Landau-Zener tunneling using time-varying elements

Landau-Zener tunneling (LZT) is a fundamental dynamical phenomenon, ubiquitous in various quantum systems. Here, we propose a time-varying electric circuit to address the question of whether the quantum LZT can occur in classical systems. Although the underlying differential equation of motion is quite different from the Schr\"odinger equation and the instantaneous frequency spectrum of the proposed circuit is not linear, the probability of the LZT in circuits (circuit LZT for short), based on our generalized definition for norm-unconserved systems, still follows the laws of the LZT in quantum systems, codetermined by the linear sweeping rate $\alpha'$ and the frequency gap $\Delta$, i.e., approaching the analytical value $\exp(-\pi\Delta^2/2\alpha')$, regardless of whether the coupling is reciprocal or nonreciprocal. The deep relationship between the circuit LZT and its quantum counterpart can be established through a linearization and block-diagonalization process. Our proposal provides a general method for simulating time-dependent quantum models using time-varying electric circuits, which has been lacking in previous studies, and paves the way for studying more complicated LZT and other dynamical phenomena in circuits and other classical systems.

cond-mat.mes-hall↗

arXiv2025

Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems

The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part (Berry curvature) to energy fluctuations and generalized forces, respectively, in Hermitian systems, direct measurement of the QGT, which is defined using both left and right eigenstates of a non-Hermitian Hamiltonian, remains challenging. Here we develop two quantum simulation schemes to directly extract all components of the QGT in pseudo-Hermitian systems with real spectra. Each scheme independently determines the complete QGT using generalized expectation values of either the energy fluctuation operator or the generalized force operator with respect to two time-evolved states prepared through distinct nonadiabatic evolutions, thereby establishing two self-contained measurement protocols. We illustrate the validity of these schemes on two $q$-deformed two-band models: one with nontrivial topology and the other with a nonvanishing off-diagonal quantum metric. Numerical simulations demonstrate that, for suitably chosen nonadiabatic ramp velocities, both schemes achieve high-fidelity agreement with theoretical predictions for measuring the QGT in both models and successfully capture the topological phase transition of the first model using Chern numbers calculated from Berry curvatures. For larger velocities, the generalized force scheme yields greater accuracy for the real part of the QGT, while the energy fluctuation scheme better captures its imaginary part. This work establishes a framework for extending dynamical measurement schemes from Hermitian to pseudo-Hermitian systems with real spectra.

quant-ph↗

arXiv2025

Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices

We investigate the ground-state and dynamical properties of ultracold Bose gases in optical lattices with a quasicrystal structure, inspired by recent experiments on twisted bilayer and quasicrystalline optical lattices. The interplay between on-site repulsive interactions and the quasiperiodic potential leads to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose-glass (BG) phase-characterized by disconnected superfluid (SF) regions-into a robust SF phase with a percolated network of SF clusters. This transition is quantitatively identified via the percolation probability. At higher filling factors, we uncover a reentrant behavior: with increasing interaction, the system first changes from BG to SF, but further strengthening reverses the trend, restoring the BG phase. This reentrance originates from an interaction-driven rearrangement of particles, where a percolated SF network fragments into isolated SF islands as repulsion dominates. The quench dynamics show distinct transient features: intraphase quenches cause minor variations in the percolation probability and the inverse participation ratio (IPR), while interphase quenches produce strong responses. In particular, an SF-to-BG quench exhibits an abrupt loss of global SF connectivity, whereas a BG-to-SF quench shows oscillatory percolation and a gradual IPR decrease, stabilizing the SF phase. These results elucidate the competition between quasiperiodicity and interactions in ultracold Bose gases and offer insights relevant to current experiments with twisted bilayer and quasicrystal optical lattices.

cond-mat.quant-gas↗

arXiv2025

Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder

Non-Hermiticity naturally breaks down the adiabaticity and thus leads to non-Abelian behaviors in multi-band systems. Here, we study how non-Abelian properties emerge in non-Hermitian systems by considering a multi-band non-Hermitian model -- the nonreciprocal Su-Schrieffer-Heeger (SSH) ladder that is formed by coupling two nonreciprocal SSH chains. Under periodic boundary conditions, we analytically obtain the exact phase diagrams of the geometry of band structure classified by its complex value and gap type, and of the non-Abelian topology based on a newly defined gauge-invariant winding number under the chiral symmetry. Under open boundary conditions, we find that the bulk-boundary correspondence survives in the thermodynamic limit but breaks down for finite sizes along with the emergence of critical non-Hermitian skin effects when the inter-leg coupling is weak, where the decaying length $\xi$ of the bulk skin modes varies with the system size $L$, satisfying the scale-free power law $\xi\propto L$. Finally, we demonstrate the non-Abelian dynamics of a Bloch state subject to an external constant force in the pseudo-Hermitian symmetric regime in comparison with the non-Hermitian Wilson lines. Our work may stimulate further interests in nontrivial non-Abelian behaviors in non-Hermitian and open quantum systems.

cond-mat.mes-hall↗

arXiv2023

Measurement-induced integer families of critical dynamical scaling in quantum many-body systems

A quantum many-body system can undergo transitions in the presence of continuous measurement. In this work, we find that a generic class of critical dynamical scaling behavior can emerge at these measurement-induced transitions. Remarkably, depending on the symmetry that can be respected by the system, different integer families of dynamical scaling can emerge. The origin of these scaling families can be traced back to the presence of hierarchies of high order exceptional points in the effective non-Hermitian descriptions of the systems. Direct experimental observation of this class of dynamical scaling behavior can be readily achieved using ultracold atoms in optical lattices or through intermediate-scale quantum computing systems.

cond-mat.quant-gas↗

arXiv2023

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-Andr\'e-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.

cond-mat.dis-nn↗

arXiv2022

Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity. Notably, We find a class of discrete breathers that aggregate to one boundary, here named as skin discrete breathers (SDBs). The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP. Specifically, the response of nonlinear energy to the perturbation is given by $E_m\propto \varGamma^{\alpha_{m}}$, where $\alpha_m=3^{m-1}$ is the power with $m=1,\cdots,L$ labeling the nonlinear energy bands. This is in sharp contrast to the $L$-th root of a linear perturbation in general. These SDBs decay in a double-exponential manner, unlike the edge states or skin modes in linear systems, which decay exponentially. Furthermore, these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity. They are also stable, as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis. As nonreciprocal nonlinear models may be experimentally realized in various platforms, such as the classical platform of optical waveguides, where Kerr nonlinearity is naturally present, and the quantum platform of optical lattices with Bose-Einstein condensates, our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity, particularly on high-order EPs, and benchmark the relevant simulations.

quant-ph↗

arXiv2022

Topological Transitions with an Imaginary Aubry-Andre-Harper Potential

We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper (AAH) potentials. Such lattices can host edge states with purely imaginary eigenenergies, which differ from the edge states of the Hermitian AAH model and are stabilized by a non-Hermitian particle-hole symmetry. The edge states arise when the period of the imaginary potential is a multiple of four lattice constants. They are topological in origin, and can manifest on domain walls between lattices with different modulation periods and phases, as predicted by a bulk polarization invariant. Interestingly, the edge states persist and remain localized even if the real line gap closes. These features can be used in laser arrays to select topological lasing modes under spatially extended pumping.

quant-ph↗

arXiv2022

Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers

We propose a general quantum circuit based on the swap test for measuring the quantity $\langle \psi_1 | A | \psi_2 \rangle$ of an arbitrary operator $A$ with respect to two quantum states $|\psi_{1,2}\rangle$. This quantity is frequently encountered in many fields of physics, and we dub it the generalized expectation as a two-state generalization of the conventional expectation. We apply the circuit, in the field of non-Hermitian physics, to the measurement of generalized expectations with respect to left and right eigenstates of a given non-Hermitian Hamiltonian. To efficiently prepare the left and right eigenstates as the input to the general circuit, we also develop a quantum circuit via effectively rotating the Hamiltonian pair $(H,-H^\dagger)$ in the complex plane. As applications, we demonstrate the validity of these circuits in the prototypical Su-Schrieffer-Heeger model with nonreciprocal hopping by measuring the Bloch and non-Bloch spin textures and the corresponding winding numbers under periodic and open boundary conditions (PBCs and OBCs), respectively. The numerical simulation shows that non-Hermitian spin textures building up these winding numbers can be well captured with high fidelity, and the distinct topological phase transitions between PBCs and OBCs are clearly characterized. We may expect that other non-Hermitian topological invariants composed of non-Hermitian spin textures, such as non-Hermitian Chern numbers, and even significant generalized expectations in other branches of physics would also be measured by our general circuit, providing a different perspective to study novel properties in non-Hermitian as well as other physics realized in qubit systems.

quant-ph↗

arXiv2022

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.

cond-mat.quant-gas↗

arXiv2021

Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping

We investigate the ground state and quantum dynamics of an interacting bosonic chain with the nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, the ground state can support Mott insulators in systems with noninteger filling due to the competition between nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from their Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be nonconserved in the non-Hermitian quantum dynamics. To systematically identify the non-Hermitian conservation law, we establish a generic approach for constructing the conserved quantities in non-Hermitian many-body quantum systems with completely real spectra, and illustrate it concretely by the system under study. The direct experimental observation of Mott insulators in systems with noninteger filling and non-Hermitian conservation laws can be performed by ultracold atoms in optical lattices with the engineered nonreciprocal hopping.

cond-mat.mes-hall↗

arXiv2021

Non-Hermitian topological end breathers

Nonlinearities in lattices with topologically nontrivial band structures can give rise to topological solitons, whose properties differ from both conventional lattice solitons and linear topological boundary states. We show that a Su-Schrieffer-Heeger-type lattice with both nonlinearity and nonreciprocal non-Hermiticity hosts a novel oscillatory soliton, which we call a topological end breather. The end breather is strongly localized to a self-induced topological domain near the end of the lattice, in sharp contrast to the extended topological solitons previously found in one-dimensional lattices. Its stable oscillatory dynamics can be interpreted as a Rabi oscillation between two self-induced topological boundary states, emerging from a combination of chiral lattice symmetry and the non-Hermitian skin effect. This demonstrates that non-Hermitian effects can give rise to a wider variety of topological solitons than was previously known to exist.

quant-ph↗

arXiv2020

Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions

For non-Hermitian quantum models, the dynamics is apparently not reflected by the static properties, e.g., the complex energy spectrum, because of the nonorthogonality of the right eigenvectors, the nonunitarity of the time evolution, the breakdown of the adiabatic theory, etc., but in experiments the time evolution of an initial state is commonly used. Here, we pay attention to the dynamics of an initial end state in nonreciprocal Su-Schrieffer-Heeger models under open boundary conditions, and we find that it is dynamically more robust than its Hermitian counterpart, because the non-Hermitian skin effect can suppress the part leaking to the bulk sites. To observe this, we propose a classical electric circuit with only a few passive inductors and capacitors, the mapping of which to the quantum model is established. This work explains how the non-Hermitian skin effect enhances the robustness of the topological end state, and it offers an easy way, via the classical electric circuit, of studying the nonreciprocal quantum dynamics, which may stimulate more dynamical studies of non-Hermitian models in other platforms.

quant-ph↗

arXiv2020

Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models

Non-Hermitian quantum many-body systems are a fascinating subject to be explored. Using the generalized density matrix renormalisation group method and complementary exact diagonalization, we elucidate the many-body ground states and dynamics of a 1D interacting non-Hermitian Aubry-Andre-Harper model for bosons. We find stable ground states in the superfluid and Mott insulating regimes under wide range of conditions in this model. We reveal a skin superfluid state induced by the non-Hermiticity from the nonreciprocal hopping. We investigate the topology of the Mott insulating phase and find its independence of the non-Hermiticity. The topological Mott insulators in this non-Hermitian system are characterized by four equal Chern numbers and a quantized shift of biorthogonal many-body polarizations. Furthermore, we show generic asymmetric expansion and correlation dynamics in the system.

cond-mat.quant-gas↗

arXiv2019

Non-Hermitian Topological Anderson Insulators

Non-Hermitian systems can exhibit unique topological and localization properties. Here we elucidate the non-Hermitian effects on disordered topological systems by studying a non-Hermitian disordered Su-Schrieffer-Heeger model with nonreciprocal hoppings. We show that the non-Hermiticity can enhance the topological phase against disorders by increasing energy gaps. Moreover, we uncover a topological phase which emerges only under both moderate non-Hermiticity and disorders, and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes. Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators. We also find that the system has non-monotonous localization behaviour and the topological transition is accompanied by an Anderson transition. These properties are general in other non-Hermitian models.

quant-ph↗

arXiv2019

Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices

Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a \textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-Andr\'{e} model, and a \textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a \textit{bulk-bulk} correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.

cond-mat.mes-hall↗