arXiv subjects

Xi-Wen Guan

Publications and source records attributed to Xi-Wen Guan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model

Although the one dimensional (1D) repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking. In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following: (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin incoherent Luttinger liquid (SILL). We investigate the universal properties and the asymprotic of correlation functions of the SILL. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the Contact susceptibilities and the variations of density, magnetization and entropy with respect to the interaction strength. As an application of these concepts, which hold true for higher dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle.

cond-mat.str-el↗

arXiv2022

Scaling of energy and power in a large quantum battery-charger model

We investigate a multi-qubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy $E_B(t)$, power $P_B(t)$ and their maximum values, $E_B^{\rm max}$ and $P_B^{\rm max}$, of the battery part by means of the antiferromagnetic Holstein-Primakoff (AFM-HP) transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of $P_B^{\rm max}$ ensues. By further combining these with the ones obtained via exact diagonalization (ED), we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10,000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with growing number of charger qubits, or when both parts simultaneously grow, we classify the system size scalings of $E_B^{\rm max}$ and $P_B^{\rm max}$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of $P_B^{\rm max}$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings.

quant-ph↗

arXiv2022

New trends in quantum integrability: Recent experiments with ultracold atoms

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.

cond-mat.quant-gas↗

arXiv2022

Excitation Spectra of one-dimensional spin-1/2 Fermi gas with an attraction

Using exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang-Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitations, hole excitations and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in spin sector and the application of the Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.

cond-mat.quant-gas↗

arXiv2022

Spin-charge separation in a 1D Fermi gas with tunable interactions

Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one-dimension to realize the Tomonaga-Luttinger liquid model describing the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge wave for various strength of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the Tomonaga-Luttinger liquid theory, and furthermore, we find that the spin excitations become dispersive at large interaction, signaling the onset of the nonlinear Luttinger liquid regime.

cond-mat.quant-gas↗

arXiv2022

Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain

We solve few-magnon problems for a finite-size spin-$S$ periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.

cond-mat.stat-mech↗

arXiv2022

Quantum dynamics of Gaudin magnets

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin-spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of Gaudin type.

cond-mat.str-el↗

arXiv2021

Multi-particle quantum walks and Fisher information in one-dimensional lattices

Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D) lattices. However the roles of interaction and quantum statistics in such a kind of walks are little known at a many-body level. In this letter, using time-evolving block decimation algorithm and many-body perturbation theory we rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs) for three indistinguishable bosons and fermions in 1D lattices. We show that such strongly correlated many-body QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states, two- and three-body bound states, but also present a quantum enhanced precision measurement of the gravitational force. It turns out that in contrast to the walks of the fermions, the QWs of three bosons exhibit richer dynamics of co-walkings and competitive Bloch oscillations, which remarkably present a surprising time scaling $t^3$ of FI below a characteristic time $t_0$ and saturate to the fundamental limit of $t^2$ for $t>t_0$.

cond-mat.quant-gas↗

arXiv2021

Lower and upper bounds of quantum battery power in multiple central spin systems

We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with "quantum battery" we refer to the central spins, whereas the bath serves as the "charger". For the single central-spin battery, we analytically derive the time evolutions of the energy transfer and the charging power with arbitrary number of bath spins. For the case of multiple central spins in the battery, we find the scaling-law relation between the maximum power $P_{max}$ and the number of central spins $N_B$. It approximately satisfies a scaling law relation $P_{max}\propto N_{B}^α$, where scaling exponent $α$ varies with the bath spin number $N$ from the lower bound $α=1/2$ to the upper bound $α=3/2$. The lower and upper bounds correspond to the limits $N\to 1$ and $N\gg N_B$, respectively. In thermodynamic limit, by applying the Holstein-Primakoff (H-P) transformation, we rigorously prove that the upper bound is $P_{max}=0.72 B A \sqrt{N} N_{B}^{3/2}$, which shows the same advantage in scaling of a recent charging protocol based on the Tavis-Cummins model. Here $B$ and $A $ are the external magnetic field and coupling constant between the battery and the charger.

quant-ph↗

arXiv2020

Emergence and disruption of spin-charge separation in one-dimensional repulsive fermions

At low temperature, collective excitations of one-dimensional (1D) interacting fermions exhibit spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding remains challenging. Using the thermodynamic Bethe Ansatz (TBA) formalism, we analytically derive universal properties of a 1D repulsive spin-1/2 Fermi gas with arbitrary interaction strength. We show how spin-charge separation emerges from the exact TBA formalism, and how it is disrupted by the interplay between the two degrees of freedom which brings us beyond the TLL paradigm. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms.

cond-mat.quant-gas↗

arXiv2020

Separable and entangled states in the high-spin XX central spin model

It is shown in a recent preprint [arXiv:2001.10008] that the central spin model with XX-type qubit-bath coupling is integrable for a central spin $s_0=1/2$. Two types of eigenstates, separable states (dark states) and entangled states (bright states) between the central spin and the bath spins, are manifested. In this work, we show by using an operator product state approach that the XX central spin model with central spin $s_0>1/2$ and inhomogeneous coupling is partially solvable. That is, a subset of the eigenstates are obtained by the operator product state ansatz. These are the separable states and those entangled states in the single-spin-excitation subspace with respect to the fully polarized reference state. Due to the high degeneracy of the separable states, the resulting Bethe ansatz equations are found to be non-unique. In the case of $s_0=1/2$ we show that all the separable and entangled states can be written in terms of the operator product states, recovering the results in [arXiv:2001.10008]. Moreover, we also apply our method to the case of homogeneous coupling and derive the corresponding Bethe ansatz equations.

cond-mat.stat-mech↗

arXiv2019

Emergent ballistic transport of Bose-Fermi mixtures in one dimension

The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel realization of two decoupled Luttinger liquids with bosonic and fermionic degrees of freedom at low temperatures. However, the transport properties of such decoupled Luttinger liquids of charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties of one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves of two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction point $x=0$. Using the Bethe ansatz solution, we first rigorously prove the existence of conserved charges for both the bosonic and fermionic degrees of freedom, preserving the Euler-type continuity equations. We then analytically obtain the distributions of the densities and currents of the local conserved quantities which solely depend on the ratio $ξ=x/t$. The left and right moving quasiparticle excitations of the two halves form multiple segmented light-cone hydrodynamics that display ballistic transport of the conserved charge densities and currents in different degrees of freedom. Our analytical results provide a deep understanding of the quantum transport of multi-component Luttinger liquids in quantum systems with both bosonic and fermionic statistics.

cond-mat.quant-gas↗

arXiv2019

Grüneisen parameters for Lieb-Liniger and Yang-Gaudin models

Using the Bethe ansatz solution, we analytically study expansionary, magnetic and interacting Grüneisen parameters (GPs) for one-dimensional (1D) Lieb-Liniger and Yang-Gaudin models. These different GPs elegantly quantify the dependences of characteristic energy scales of these quantum gases on the volume, the magnetic field and the interaction strength, revealing the caloric effects resulted from the variations of these potentials. The obtained GPs further confirm an identity which is incurred by the symmetry of the thermal potential. We also present universal scaling behavior of these GPs in the vicinities of the quantum critical points driven by different potentials. The divergence of the GPs not only provides an experimental identification of non-Fermi liquid nature at quantum criticality but also elegantly determine low temperature phases of the quantum gases. Moreover, the pairing and depairing features in the 1D attractive Fermi gases can be captured by the magnetic and interacting GPs, facilitating experimental observation of quantum phase transitions. Our results open to further study the interaction- and magnetic-field-driven quantum refrigeration and quantum heat engine in quantum gases of ultracold atoms.

cond-mat.quant-gas↗

arXiv2019

Grüneisen Parameters: origin, identity and quantum refrigeration

In solid state physics, the Grüneisen parameter (GP), originally introduced in the study of the effect of changing the volume of a crystal lattice on its vibrational frequency, has been widely used to investigate the characteristic energy scales of systems with respect to the changes of external potentials. On the other hand, the GP is little investigated in a strongly interacting quantum gas systems. Here we report on our general results on the origin of GP, new identity and caloric effects in quantum gases of ultracold atoms. We prove that the symmetry of the dilute quantum gas systems leads to a simple identity among three different types of GPs, quantifying caloric effect induced respectively by variations of volume, magnetic field and interaction. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Femi gases. Based on the exact equations of states of these systems, we obtain analytic results for the singular behaviour of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp-up and -down in quantum gases provides a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid state materials.

cond-mat.quant-gas↗

arXiv2019

Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation, and discuss the phase transitions between the two SPT phases and their experimental signatures.

cond-mat.quant-gas↗

arXiv2019

Exact Entanglement dynamics in Three Interacting Qubits

Motivated by recent experimental study on coherent dynamics transfer in three interacting atoms or electron spins \cite{Barredo:2015,Rosenfeld:2018}, here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. So that dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer, characterized by the quantum mutual information and concurence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.

quant-ph↗

arXiv2019

Exact quantum dynamics of XXZ central spin problems

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $Δ$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=Δ=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{πN}{A} m$ for a large $N$. For $Δ=0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity.

quant-ph↗

arXiv2019

Professor Chen Ping Yang's early significant contributions to mathematical physics

In the 60's Professor Chen Ping Yang with Professor Chen Ning Yang published several seminal papers on the study of Bethe's hypothesis for various problems of physics. The works on the lattice gas model, critical behaviour in liquid-gas transition, the one-dimensional (1D) Heisenberg spin chain, and the thermodynamics of 1D delta-function interacting bosons are significantly important and influential in the fields of mathematical physics and statistical mechanics. In particular, the work on the 1D Heisenberg spin chain led to subsequent developments in many problems using Bethe's hypothesis. The method which Yang and Yang proposed to treat the thermodynamics of the 1D system of bosons with a delta-function interaction leads to significant applications in a wide range of problems in quantum statistical mechanics. The Yang and Yang thermodynamics has found beautiful experimental verifications in recent years.

physics.hist-ph↗