arXiv subjects

Shu Chen

Publications and source records attributed to Shu Chen.

At least 91 records · Page 5Linked to original sources

arXiv2023

Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.

quant-ph↗

arXiv2023

Detecting entanglement in quantum many-body systems via permutation moments

Multipartite entanglement plays an essential role in both quantum information science and many-body physics. Due to the exponentially large dimension and complex geometric structure of the state space, the detection of entanglement in many-body systems is extremely challenging in reality. Conventional means, like entanglement witness and entropy criterion, either highly depend on the prior knowledge of the studied systems or the detection capability is relatively weak. In this work, we propose a framework for designing multipartite entanglement criteria based on permutation moments, which have an effective implementation with either the generalized control-SWAP quantum circuits or the random unitary techniques. These criteria show strong detection capability in the multi-qubit Ising model with a long-range $XY$ Hamiltonian. The quantities associated with these criteria have clear physical meaning and can be used as entanglement quantifiers, with which we show the entanglement scaling transition in a quantum dynamical phase transition. Furthermore, our framework can also be generalized to detect the much more complicated entanglement structure in quantum many-body systems.

quant-ph↗

arXiv2022

Absence of logarithmic and algebraic scaling entanglement phases due to skin effect

Measurement-induced phase transition in the presence of competition between projective measurement and random unitary evolution has attracted increasing attention due to the rich phenomenology of entanglement structures. However, in open quantum systems with free fermions, a generalized measurement with conditional feedback can induce skin effect and render the system short-range entangled without any entanglement transition, meaning the system always remains in the ``area law'' entanglement phase. In this work, we demonstrate that the power-law long-range hopping does not alter the absence of entanglement transition brought on by the measurement-induced skin effect for systems with open boundary conditions. In addition, for the finite-size systems, we discover an algebraic scaling $S(L, L/4)\sim L^{3/2-p}$ when the power-law exponent $p$ of long-range hopping is relatively small. For systems with periodic boundary conditions, we find that the measurement-induced skin effect disappears and observe entanglement phase transitions among ``algebraic law'', ``logarithmic law'', and ``area law'' phases.

quant-ph↗

arXiv2022

Observation of size-dependent boundary effects in non-Hermitian electric circuits

The non-Hermitian systems with the non-Hermitian skin effect (NHSE) are very sensitive to the imposed boundary conditions and lattice size, which leads to size-dependent non-Hermitian skin effects. Here, we report the experimental observation of NHSE with different boundary conditions and different lattice size in a unidirectional hopping model based on a circuit platform. The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary. Meanwhile, our experimental results show how the lattice size and boundary terms together affect the strength of NHSE. Therefore, our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems.

quant-ph↗

arXiv2022

Fundamental Limitation on the Detectability of Entanglement

Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to theoretically evaluate the detection capability of entanglement criteria. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double-exponentially. Furthermore, if multi-copy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems.

quant-ph↗

arXiv2022

The simulation of non-Hermitian disordered system in linear circuits

Non-Hermitian skin effect (NHSE) is a novel phenomenon appearing in non-Hermitian systems. Here, we report the experimental observation of NHSE. Different from the previous non-reciprocal circuit implementation scheme using logic components, we construct our one-dimensional (1D) circuits using linear components only. Besides, we achieve the non-reciprocity by proportionally varying the parameter value of the components. By measuring the voltage response of each site, the information of eigenstates can be mapped out. The results show that the voltage response is always larger on one end of the circuit no matter on which end voltage driving is applied, indicating clearly the presence of the NHSE. Furthermore, we also simulate the interplay of NHSE and Anderson localization (AL) when additional disorder is introduced. Upon increasing the disorder strength, we observe the transformation from the skin effect phase to the localized phase. In the regime of skin effect phase, the eigenstates are all localized at one edge while eigenstates are affected by the voltage supply input in localized phase. Our findings unveil a possible new route for simulation of topological phenomena in non-Hermitian systems.

cond-mat.dis-nn↗

arXiv2022

Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo

We unveil the role of the long time average of Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long time average of Loschmidt echo. The nonanalytic behaviours are illustrated by a sharp change in the long time average of Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of rate function and fidelity susceptibility is also discussed.

quant-ph↗

arXiv2022

Evolution of topological end states in the one-dimensional Kondo-Heisenberg model with site modulation

We investigate the interplay of the topological and Kondo effects in a one-dimensional Kondo-Heisenberg model with nontrivial conduction band using the density matrix renormalization group method. By analyzing the density profile, the local hybridization, and the spin/charge gap, we find that the Kondo effect can be destructed at the edges of the chain by the topological end state below a finite critical Kondo coupling $J_{K}^{c}$. We construct a phase diagram characterizing the transition of the end states.

cond-mat.str-el↗

arXiv2022

Structure-Aware NeRF without Posed Camera via Epipolar Constraint

The neural radiance field (NeRF) for realistic novel view synthesis requires camera poses to be pre-acquired by a structure-from-motion (SfM) approach. This two-stage strategy is not convenient to use and degrades the performance because the error in the pose extraction can propagate to the view synthesis. We integrate the pose extraction and view synthesis into a single end-to-end procedure so they can benefit from each other. For training NeRF models, only RGB images are given, without pre-known camera poses. The camera poses are obtained by the epipolar constraint in which the identical feature in different views has the same world coordinates transformed from the local camera coordinates according to the extracted poses. The epipolar constraint is jointly optimized with pixel color constraint. The poses are represented by a CNN-based deep network, whose input is the related frames. This joint optimization enables NeRF to be aware of the scene's structure that has an improved generalization performance. Extensive experiments on a variety of scenes demonstrate the effectiveness of the proposed approach. Code is available at https://github.com/XTU-PR-LAB/SaNerf.

cs.CV↗

arXiv2022

Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices

We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-André model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-André model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.

cond-mat.dis-nn↗

arXiv2022

Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization

We carry out a systematical study of the size scaling of Liouvillian gap in boundary-dissipated one-dimensional quasiperiodic and disorder systems. By treating the boundary-dissipation operators as a perturbation, we derive an analytical expression of the Liouvillian gap, which indicates clearly the Liouvillian gap being proportional to the minimum of boundary densities of eigenstates of the underlying Hamiltonian, and thus give a theoretical explanation why the Liouvillian gap has different size scaling relation in the extended and localized phase. While the Liouvillian gap displays a power-law size scaling $Δ_{g}\propto L^{- 3}$ in the extended phase, our analytical result unveils that the Liouvillian gap fulfills an exponential scaling relation $Δ_{g}\propto e^{- κL}$ in the localized phase, where $κ$ takes the largest Lyapunov exponent of localized eigenstates of the underlying Hamiltonian. By scrutinizing the extended Aubry-André-Harper model, we numerically confirm that the Liouvillian gap fulfills the exponential scaling relation and the fitting exponent $κ$ coincides pretty well with the analytical result of Lyapunov exponent. The exponential scaling relation is further verified numerically in other one-dimensional quasiperiodic and random disorder models. We also study the relaxation dynamics and show the inverse of Liouvillian gap giving a reasonable timescale of asymptotic convergence to the steady state.

cond-mat.dis-nn↗

arXiv2022

Knot topology of exceptional point and non-Hermitian no-go theorem

Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory. In this paper, we provide a topological classification of isolated EPs based on homotopy theory. In particular, the classification indicates that an $n$-th order EP in two dimensions is fully characterized by the braid group B$_n$, with its eigenenergies tied up into a geometric knot along a closed path enclosing the EP. The quantized discriminant invariant of the EP is the writhe of the knot. The knot crossing number gives the number of bulk Fermi arcs emanating from each EP. Furthermore, we put forward a non-Hermitian no-go theorem, which governs the possible configurations of EPs and their splitting rules on a two-dimensional lattice and goes beyond the previous fermion doubling theorem. We present a simple algorithm generating the non-Hermitian Hamiltonian with a prescribed knot. Our framework constitutes a systematic topological classification of the EPs and paves the way towards exploring the intriguing phenomena related to the enigmatic non-Hermitian band degeneracy.

cond-mat.mes-hall↗

arXiv2022

Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers

Quantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a new tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the newly developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and may trigger further investigations on various quantum and topological phenomena.

quant-ph↗

arXiv2022

Symmetry and topological classification of Floquet non-Hermitian systems

Recent experimental advances in Floquet engineering and controlling dissipation in open systems have brought about unprecedented flexibility in tailoring novel phenomena without any static and Hermitian analogues. It can be epitomized by the various Floquet and non-Hermitian topological phases. Topological classifications of either static/Floquet Hermitian or static non-Hermitian systems based on the underlying symmetries have been well established in the past several years. However, a coherent understanding and classification of Floquet non-Hermitian (FNH) topological phases have not been achieved yet. Here we systematically classify FNH topological bands for 54-fold generalized Bernard-LeClair (GBL)symmetry classes and arbitrary spatial dimensions using $K$-theory. The classification distinguishes two different scenarios of the Floquet operator's spectrum gaps [dubbed as Floquet operator (FO) angle-gapped and FO angle-gapless]. The results culminate into two periodic tables, each containing 54-fold GBL symmetry classes. Our scheme reveals FNH topological phases without any static/Floquet Hermitian and static non-Hermitian counterparts. And our results naturally produce the periodic tables of Floquet Hermitian topological insulators and Floquet unitaries. The framework can also be applied to characterize the topological phases of bosonic systems. We provide concrete examples of one and two-dimensionalfermionic/bosonic systems. And we elucidate the meaning of the topological invariants and their physical consequences. Our paper lays the foundation for a comprehensive exploration of FNH topological bands. And it opens a broad avenue toward uncovering unique phenomena and functionalities emerging from the synthesis of periodic driving, non-Hermiticity, and band topology.

cond-mat.mes-hall↗

arXiv2022

Dynamic quantum-enhanced sensing without entanglement in central spin systems

We propose a dynamic quantum sensing scheme by using a quantum many-spin system composed of a central spin interacting with many surrounding spins. Starting from a generalized Ising ring model, we investigate the error propagation formula of the central spin and it indicates that Heisenberg scaling can be reached while the probe state only needs to be a product state. Particularly, we derive an analytical form of the dynamic quantum Fisher information in a limit case, which explicitly exhibits the Heisenberg scaling. By comparing with numerical results, we demonstrate that the general case can be well approximated by the analytical result when the coupling strength among the surrounding spins is much weaker than the coupling strength between the central and surrounding spins. This analytic result guides us to find the appropriate probe state and the proper measurement time, to achieve the Heisenberg scaling in realistic situations. Furthermore, we investigate various effects which are important in practical quantum systems, including the central spin Zeeman term, the anisotropy of the hyperfine interaction and the inhomogeneity of the hyperfine coupling strength. Our result indicates that the dynamic quantum-enhanced sensing scheme seems feasible in realistic quantum central spin systems, like semiconductor quantum dots.

quant-ph↗

arXiv2022

Real-space nanoimaging of THz polaritons in the topological insulator Bi2Se3

Plasmon polaritons in topological insulators attract attention from a fundamental perspective and for potential THz photonic applications. Although polaritons have been observed by THz far-field spectroscopy on topological insulator microstructures, real-space imaging of propagating THz polaritons has been elusive so far. Here, we show spectroscopic THz near-field images of thin Bi2Se3 layers (prototypical topological insulators) revealing polaritons with up to 12 times increased momenta as compared to photons of the same energy and decay times of about 0.48 ps, yet short propagation lengths. From the images we determine and analyze the polariton dispersion, showing that the polaritons can be explained by the coupling of THz radiation to various combinations of Dirac and massive carriers at the Bi2Se3 surfaces, massive bulk carriers and optical phonons. Our work provides critical insights into the nature of THz polaritons in topological insulators and establishes instrumentation and methodology for imaging of THz polaritons.

physics.optics↗

arXiv2022

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

We study one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as the periodical system when the hopping parameters fulfill certain conditions, whereas eigenstates display non-Hermitian skin effect.

cond-mat.stat-mech↗

arXiv2021

Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals

The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs. While most of the previous studies are concerned with one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this work, we disclose an exactly solvable 2D quasicrystal model with parity-time ($\mathcal{PT}$) symmetry displaying exact MEs. In the thermodynamic limit, we unveil that the extended-localized transition point, observed at the $\mathcal{PT}$ symmetry breaking point, is topologically characterized by a hidden winding number defined in the dual space. The coupling waveguide platform can be used to realize the 2D non-Hermitian quasicrystal model, and the excitation dynamics can be used to detect the localization features.

cond-mat.dis-nn↗