arXiv subjects

Xi-Wen Guan

Publications and source records attributed to Xi-Wen Guan.

At least 19 recordsLinked to original sources

arXiv2026

Universal Transport Properties of Continuous Quantum Gases

The Drude weight characterizes ballistic transport in quantum many-body systems. Although analytical calculations of Drude weights have been extensively studied in integrable models, their direct connections to finite-temperature macroscopic state functions remain unestablished, especially for continuous multicomponent quantum gases. In the present work, we use generalized hydrodynamics and the thermodynamic Bethe ansätz to calculate exactly the Drude weights for one-dimensional continuous integrable systems, including the Lieb-Liniger and Bose-Fermi mixture models. We derive universal exact relations between Drude weight matrix components and key thermodynamic densities (particle density, enthalpy, entropy). Analytic expressions for Drude weight are obtained across different physical regimes, i.e. strong- and weak-coupling regimes in addition to universal scaling laws near the quantum phase transitions. To bridge theory and experiment, we simulate two experimental protocols, linear potential quench and bipartitioning quench, to enable reliable measurements of the Drude weights. Using these protocols, we calculate the charge and energy Drude weight for Lieb-Liniger gas and compare with recent measurements reported in [Science 391, 290 (2026)], showing excellent agreement with particle density and enthalpy, respectively, thus offering deeper physical insights into experimental observations. Our findings directly link ballistic transport properties to thermodynamics, providing rigorous theoretical benchmarks for future ultracold atomic gas experiments.

cond-mat.quant-gas↗

arXiv2026

Tomonaga-Luttinger liquid theory for one-dimensional attractive Fermi gases

The one-dimensional (1D) Yang-Gaudin model-an integrable $δ$-function interacting Fermi gas, serves as a paradigm in quantum many-body physics, encompassing phenomena from spin-charge separation to the Luther-Emery liquid. However, a consistent description of the Luther-Emery liquid and the bosonization of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing states in the 1D attractive Fermi gas remains elusive. In this work, we develop a universal Tomonaga-Luttinger liquid (TLL) theory to describe the FFLO state across both weak and strong coupling regimes. We rigorously derive the low-energy effective Hamiltonian using bosonization, revealing the emergence of a two-component Luttinger liquid: one exhibiting spin-charge coupling in the weakly attractive regime, and another featuring charge-charge separation in the strongly attractive regime. For the weakly attractive regime, we further derive the renormalization-group equations for the sine-Gordon term in the spin sector and show that this term undergoes a relevant-irrelevant phase transition driven by the magnetic field. For the strongly attractive regime, we analyze the dynamical correlation functions of the FFLO pairing state based on the derived effective Hamiltonian. Finally, we propose an experimental scheme using ultracold atoms to verify the Luther-Emery liquid behavior and the subtle phenomena of spin-charge coupling and charge-charge separation.

cond-mat.quant-gas↗

arXiv2026

Kaleidoscope Yang-Baxter Equation for Gaudin's Kaleidoscope models

Recently, researchers have proposed the Asymmetric Bethe ansatz method - a theoretical tool that extends the scope of Bethe ansatz-solvable models by "breaking" partial mirror symmetry via the introduction of a fully reflecting boundary. Within this framework, the integrability conditions which were originally put forward by Gaudin have been further generalized. In this work, building on Gaudin's generalized kaleidoscope model, we present a detailed investigation of the relationship between DN symmetry and its integrability. We demonstrate that the mathematical essence of integrability in this class of models is characterized by a newly proposed Kaleidoscope Yang-Baxter Equation. Furthermore, we show that the solvability of a model via the coordinate Bethe ansatz depends not only on the consistency relations satisfied by scattering matrices, but also on the model's boundary conditions and the symmetry of the subspace where solutions are sought. Through finite element method based numerical studies, we further confirm that Bethe ansatz integrability arises in a specific symmetry sector. Finally, by analyzing the algebraic structure of the Kaleidoscope Yang-Baxter Equation, we derive a series of novel quantum algebraic identities within the framework of quantum torus algebra.

nlin.SI↗

arXiv2025

Low Energy Excitations of a 1D Fermi Gas with Attractive Interactions

The low-energy excitations of a two-component repulsive Fermi gas confined to one dimension are linear dispersing spin- and charge-density waves whose respective propagation velocities depend on the strength and sign of their interaction. Quasi-1D fermions with attractive interaction realize the Luther-Emery liquid, which exhibits a rich array of phenomena, many of which are qualitatively different from those exhibited by their repulsive counterpart. We use a Feshbach resonance to access attractive interactions with $^6$Li atoms. We measured the spin and charge dynamic structure factors using Bragg spectroscopy and find that, contrary to repulsive interactions, the spin wave propagates faster than the charge density wave, thus producing an inversion of the classic spin-charge separation. We also find that a small spin polarization strongly suppresses the spin gap in the measured Bragg spectra. Evidence for pairing are a reduction in spin correlations with increasing attraction and RF spectra consistent with an atom/molecule mixture.

cond-mat.quant-gas↗

arXiv2025

Universal scaling of higher-order cumulants in quantum isotropic spin chains

Understanding universal behavior of far-from-equilibrium transport dynamics at a quantum many body level is a longstanding challenge. In particular, a full characterization of universal dynamics of nonlocal correlation functions still remains largely unknown. In this letter, we uncover universal scaling laws of higher-order cumulants in one-dimensional isotropic Heisenberg model, revealing anomalous behaviors of nonequilibrium dynamics exclusively accessible in higher-order correlations. By means of numerical simulations and full counting statistics, we determine the power laws of both the spin polarization transfer and contrast cumulants for different kinds of helix and domain-wall initial states. Building on such physical states, we unify the scaling behavior of the higher-order cumulants, giving rise to two types of dynamics: anomalous diffusive and superdiffusive. For the former, these higher cumulants show a deviation from Gaussian statistics, with the scaling exponents being identical for the first four orders. For the latter, however, we observe a breakdown of KPZ universality, with the exponents of the third and fourth orders differing significantly from those of the first two. Our results are also agreeable with recent experimental observations, advancing understanding of far-from-equilibrium transport phenomena.

cond-mat.quant-gas↗

arXiv2025

Quantum transport in 1D Hubbard model: Drude weights and Seebeck effect

The Drude weight (DW) is an essential quantity that characterizes the quantum transport properties of many-body systems. However, a rigorous understanding and exact computation of DWs, particularly for strongly correlated systems with doping, still remain elusive. In this Letter, taking advantage of the quantum integrability, we calculate exactly the DWs and Seebeck effect (SE) for generic filling factor in one-dimensional (1D) Fermi-Hubbard model with arbitrary interaction strengths and magnetic fields. We build up its intrinsic connection to the Luttinger parameters, and derive universal scaling laws for DWs across phase transitions. Our results provide a deep understanding of mutual influences in transport between the spin and the charge degrees of freedom, showing a counterintuitive subtle spin-charge coupling effect and uncovering the microscopic origin of the (spin) Seebeck effects in thermal conductivity. Finally, we propose an experimental protocol to measure the DWs in ultracold atomic systems.

cond-mat.str-el↗

arXiv2025

Exact Spectral Function of One-Dimensional Bose Gases

Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger model. We calculate exactly the dynamical correlation functions by computing the form factor through a newly developed method, by which we are capable of calculating all possible "relative excitations" over the ground state or a finite temperature state at a high precision. Consequently, full spectral functions obtained for the model manifests the unique power-law singularity behaviour at the spectral threshold, confirming the validity of nonlinear Luttinger liquid theory. Our method advances the theory of dynamical correlation functions with high precision towards the thermodynamic limit, and is capable of benchmarking experimental observation of such novel correlated properties.

cond-mat.quant-gas↗

arXiv2025

One-body dynamical correlation function of Lieb-Liniger model at finite temperature

The dynamical correlated properties of one-dimensional (1D) Bose gases provide profound understanding of novel physics emergent from collective excitations, for instance, the breakdown of off-diagonal long-range order, and the establishment of Tomonaga-Luttinger liquid theory. However, due to the nonperturbative nature of 1D many-body systems, the exact evaluation of correlation functions is notoriously difficult. Here, by means of a form factor approach based on an algebraic Bethe ansatz and numerics, we present a thorough study on the one-body dynamical correlation function (1BDCF) of the Lieb-Liniger model at finite temperature. The influence of thermal fluctuation and interaction on the behavior of 1BDCF has been demonstrated and analyzed from various perspectives, including the spectral distribution, the line shape at fixed momentum, and the corresponding static correlations.

cond-mat.quant-gas↗

arXiv2025

Haldane Fractional Statistics for 1D Heisenberg Spin XXX Chain

Haldane's fractional exclusion statistics (FES) describes a generalized Pauli exclusion statistics, which can be regarded as an emergent quantum statistics induced by the intrinsic dynamical interaction. A non-mutual FES has been identified at the quantum criticality of the one-dimensional (1D) and 2D interacting Bose Gas [Nat. Sci. Rev. 9, nwac027 (2022)]. It is naturally asked if such a non-mutual FES can be induced by the spin-spin interaction in the antiferromagnetic spin-1/2 XXX chain? In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin XXX chain remarkably possesses the non-mutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the non-mutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also build up an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from quantum FES point of view.

cond-mat.str-el↗

arXiv2024

Exact results of one-dimensional repulsive Hubbard model

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.

cond-mat.str-el↗

arXiv2024

Microscopic origin of quantum supersonic phenomenon in one dimension

Using the Bethe ansatz (BA), we rigorously obtain non-equilibrium dynamics of an impurity with a large initial momentum $Q$ in the one-dimensional (1D) interacting bosonic medium. We show that magnon and exciton-like states obtained from the BA equations drastically determine the oscillation nature of the quantum flutter with the periodicity given by $τ_{\rm QF} = 2π/(|\varepsilon_{\rm c}(0)|- |\varepsilon_{\rm s}(0)|)$. Where the charge and spin dressed energies $\varepsilon_{\rm c,s}(0)$ are precisely given by the thermodynamical BA equations. While we further find a persistent revival dynamics of the impurity with a larger periodicity $τ_{L} = L/\left(v_{\rm c}(Q-k^*)-v_{\rm s}(k^*)\right)$ than $τ_{\rm QF}$, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length $L$, here $v_{\rm c,s}$ are the sound velocities of charge and spin excitations, respectively, and $k^*$ is a characteristic momentum of the impurity to the Fermi point. Finally, we study the application of such a magnon impurity as a quantum resource for measuring the gravitational force.

cond-mat.quant-gas↗

arXiv2024

Universal shot-noise limit for quantum metrology with local Hamiltonians

Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher information. We apply our bound to the metrological protocol requiring only separable initial states, which can be readily prepared in experiments. By establishing a link between our bound and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems, we prove that the precision cannot surpass the shot noise limit at all times in locally interacting quantum systems. This conclusion also holds for an initial state that is the non-degenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling

quant-ph↗

arXiv2024

Quantum-Enhanced Metrology in Cavity Magnomechanics

Magnons, as fundamental quasiparticles emerged in elementary spin excitations, hold a big promise for innovating quantum technologies in information coding and processing. Here we discover subtle roles of entanglement in a metrological scheme based on an experimentally feasible cavity magnomechanical system, where the magnons are responsible for sensing a weak magnetic field whereas the cavity field carries out a precision measurement of the weak field. By establishing exact relations between the Fisher information and entanglement, we show that for the weak coupling case the measurement precision can reach the Heisenberg limit, whereas quantum criticality enables us to enhance measurement precision for the strong coupling case. In particular, we also find that the entanglement between magnons and photons is of crucial importance during the dynamical encoding process, but the presence of such an entanglement in the measurement process dramatically reduces the final measurement precision.

quant-ph↗

arXiv2023

Yang-Gaudin model: A paradigm of many-body physics

Using Bethe's hypothesis, C N Yang exactly solved the one-dimensional (1D) delta-function interacting spin-1/2 Fermi gas with an arbitrary spin-imbalance in 1967. At that time, using a different method, M Gaudin solved the problem of interacting fermions in a spin-balanced case. Later, the 1D delta-function interacting fermion problem was named as the Yang-Gaudin model. It has been in general agreed that a key discovery of C N Yang's work was the cubic matrix equation for the solvability conditions. % This equation was later independently found by R J Baxter for commuting transfer matrices of 2D exactly solvable vertex models. % The equation has since been referred to Yang-Baxter equation, being the master equation to integrability. % The Yang-Baxter equation has been used to solve a wide range of 1D many-body problems in physics, such as 1D Hubbard model, $SU(N)$ Fermi gases, Kondo impurity problem and strongly correlated electronic systems etc. % In this paper, we will briefly discuss recent developments of the Yang-Gaudin model on several breakthroughs of many-body phenomena, ranging from the universal thermodynamics to the Luttigner liquid, the spin charge separation, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing state and the quantum criticality. % These developments demonstrate that the Yang-Gaudin model has laid out a profound legacy of the Yang-Baxter equation.

cond-mat.quant-gas↗

arXiv2023

Exact results of dynamical structure factor of Lieb-Liniger model

The dynamical structure factor (DSF) represents a measure of dynamical density-density correlations in a quantum many-body system. Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large Hilbert space, such kind of dynamical correlations often impose a big theoretical challenge. For one dimensional (1D) quantum many-body systems, qualitative predictions of dynamical response functions are usually carried out by using the Tomonaga-Luttinger liquid (TLL) theory. In this scenario, a precise evaluation of the DSF for a 1D quantum system with arbitrary interaction strength remains a formidable task. In this paper, we use the form factor approach based on algebraic Bethe ansatz theory to calculate precisely the DSF of Lieb-Liniger model with an arbitrary interaction strength at a large scale of particle number. We find that the DSF for a system as large as 2000 particles enables us to depict precisely its line-shape from which the power-law singularity with corresponding exponents in the vicinities of spectral thresholds naturally emerge. It should be noted that, the advantage of our algorithm promises an access to the threshold behavior of dynamical correlation functions, further confirming the validity of nonlinear TLL theory besides Kitanine et. al. 2012 J. Stat. Mech. P09001. Finally we discuss a comparison of results with the results from the ABACUS method by J.-S. Caux 2009 J. Math. Phys. 50 095214 as well as from the strongly coupling expansion by Brand and Cherny 2005 Phys. Rev. A 72 033619.

cond-mat.quant-gas↗

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↗