arXiv subjects

Xi-Wen Guan

Publications and source records attributed to Xi-Wen Guan.

At least 55 records · Page 3Linked to original sources

arXiv2018

An Interaction-Driven Many-Particle Quantum Heat Engine: Universal Behavior

A quantum heat engine (QHE) based on the interaction driving of a many-particle working medium is introduced. The cycle alternates isochoric heating and cooling strokes with both interaction-driven processes that are simultaneously isochoric and isentropic. When the working substance is confined in a tight waveguide, the efficiency of the cycle becomes universal at low temperatures and governed by the ratio of velocities of a Luttinger liquid. We demonstrate the performance of the engine with an interacting Bose gas as a working medium and show that the average work per particle is maximum at criticality. We further discuss a work outcoupling mechanism based on the dependence of the interaction strength on the external spin degrees of freedom.

quant-ph↗

arXiv2018

The spin-s homogeneous central spin model: exact spectrum and dynamics

We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s=1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of SU(2), and the other based on integrability. We also analyze the exact time evolution of a spin coherent state, and compute the time evolution of various quantities of physical interest, including the entanglement entropy, spin polarization and Loschmidt echo.

quant-ph↗

arXiv2018

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal $M$-particle correlation functions, momentum distribution and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate two-point correlation function, the large moment tail of momentum distribution and static structure factor of the model in terms of the fractional statistical parameter $α=1-2/γ$, where $γ$ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in term of the fractional statistical parameter.

cond-mat.quant-gas↗

arXiv2018

FFLO correlation and free fluids in the one-dimensional attractive Hubbard model

In this Rapid Communication we show that low energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially-polarized phase. We then show that for such a FFLO-like state in the low density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility and specific heat obey simple additivity rules, indicating the `free' particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility which provide universal macroscopic properties/dimensionless constants of interacting fermions at low energy.

cond-mat.str-el↗

arXiv2018

Universal thermodynamics of the one-dimensional attractive Hubbard model

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here by solving the thermodynamic Bethe ansatz equations we study the universal thermodynamics, quantum criticality and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent $z=2$ and correlation critical exponent $ν=1/2$ in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.

cond-mat.str-el↗

arXiv2018

Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction

We present a rigorous study of momentum distribution and p-wave contacts of one dimensional (1D) spinless Fermi gases with an attractive p-wave interaction. Using the Bethe wave function, we analytically calculate the large-momentum tail of momentum distribution of the model. We show that the leading ($\sim 1/p^{2}$) and sub-leading terms ($\sim 1/p^{4}$) of the large-momentum tail are determined by two contacts $C_2$ and $C_4$, which we show, by explicit calculation, are related to the short-distance behaviour of the two-body correlation function and its derivatives. We show as one increases the 1D scattering length, the contact $C_2$ increases monotonically from zero while $C_4$ exhibits a peak for finite scattering length. In addition, we obtain analytic expressions for p-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations in both weakly and strongly attractive regimes.

cond-mat.quant-gas↗

arXiv2018

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $Δk_F$ ($2Δk_F$). Here $Δk_F=π(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch $k=Δk_F$, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter $β$ representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.

cond-mat.str-el↗

arXiv2017

Quantum criticality of spinons

The free fermion nature of interacting spins in one dimensional (1D) spin chains still lacks a rigorous study. In this letter we show that the length-$1$ spin strings significantly dominate critical properties of spinons, magnons and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution we analytically calculate exact scaling functions of thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double peaks in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), quantum critical and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio $R_W=4K_s$ remains almost temperature-independent, here $K_s$ is the Luttinger parameter. Furthermore, applying our results we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C${}_4$H${}_4$N${}_2$)(NO${}_3$)${}_2$ recently studied in Phys. Rev. Lett. {\bf 114}, 037202 (2015)]. We further find that the magnetization peak used in experiments is not a good quantity to map out the finite temperature TLL phase boundary.

cond-mat.stat-mech↗

arXiv2017

Observation of Quantum Criticality and Luttinger Liquid in One-dimensional Bose Gases

We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.

cond-mat.quant-gas↗

arXiv2016

Dimensionless ratios: characteristics of quantum liquids and their phase transitions

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multi-component quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel --- a novel and useful characteristic of multi-component Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realised multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin-degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.

cond-mat.quant-gas↗

arXiv2016

Universal Properties of Fermi Gases in One-dimension

In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility and the contact susceptibility, giving a precise understanding of the 1D analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $χ\sim {1}/{\sqrt{T}}\exp(-Δ/T)$ at low temperatures, where $Δ$ is the energy gap and $T$ is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization $P$ and the contact $C$ for both repulsive and attractive Fermi gases. Our findings emphasize the role of the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.

cond-mat.quant-gas↗

arXiv2016

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

The correlation function is an important quantity in the physics of ultracold quantum gases because it provides information about the quantum many-body wave function beyond the simple density profile. In this paper we first study the $M$-body local correlation functions, $g_M$, of the one-dimensional (1D) strongly repulsive Bose gas within the Lieb-Liniger model using the analytical method proposed by Gangardt and Shlyapnikov [1,2]. In the strong repulsion regime the 1D Bose gas at low temperatures is equivalent to a gas of ideal particles obeying the non-mutual generalized exclusion statistics (GES) with a statistical parameter $α=1-2/γ$, i.e. the quasimomenta of $N$ strongly interacting bosons map to the momenta of $N$ free fermions via $k_i\approx αk_i^F $ with $i=1,\ldots, N$. Here $γ$ is the dimensionless interaction strength within the Lieb-Liniger model. We rigorously prove that such a statistical parameter $α$ solely determines the sub-leading order contribution to the $M$-body local correlation function of the gas at strong but finite interaction strengths. We explicitly calculate the correlation functions $g_M$ in terms of $γ$ and $α$ at zero, low, and intermediate temperatures. For $M=2$ and $3$ our results reproduce the known expressions for $g_{2}$ and $g_{3}$ with sub-leading terms (see for instance [3-5]). We also express the leading order of the short distance \emph{non-local} correlation functions $\langleΨ^\dagger(x_1)\cdotsΨ^\dagger(x_M)Ψ(y_M)\cdotsΨ(y_1)\rangle$ of the strongly repulsive Bose gas in terms of the wave function of $M$ bosons at zero collision energy and zero total momentum. Here $Ψ(x)$ is the boson annihilation operator. These general formulas of the higher-order local and non-local correlation functions of the 1D Bose gas provide new insights into the many-body physics.

cond-mat.quant-gas↗

arXiv2016

Universal low energy physics in one-dimensional multicompnent Fermi gases with a strongly repulsive $δ$-function interaction

It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperature the ground state of the one-dimensional (1D) $w$-component Fermi gas coincides with that of the spinless Bose gas in the limit $ω\to \infty$. This behaviour was experimentally evidenced through a quasi-1D tightly trapping ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198 (2014)]. However, understanding of low temperature behaviour of the Fermi gases with a repulsive interaction acquires spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic $SU(w)$ Heisenberg spin chain. Here we analytically derive universal thermodynamics of 1D strongly repulsive fermionic gases with $SU(w)$ symmetry via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the systems at low temperatures in a weak magnetic field are obtained through the Wiener-Hopf method. In particular, the free energy essentially manifests the spin-charge separated conformal field theories for the high symmetry systems with arbitrary repulsive interaction strength. We also find that the sound velocity of the Fermi gases in the large $w$ limit coincides with that for the spinless Bose gas, whereas the spin velocity vanishes quickly as $w$ becomes large. This indicates a strong suppression of the Fermi exclusion statistics by the commutativity feature among the $w$-component fermions with different spin states in the Tomonaga-Luttinger liquid phase. Moreover, the equations of state and critical behaviour of physical quantities at finite temperatures are analytically derived in terms of the polylogarithm functions in the quantum critical region.

cond-mat.quant-gas↗

arXiv2015

Itinerant ferromagnetism in 1D two-component Fermi gases

We study a one-dimensional two-component atomic Fermi gas with an infinite intercomponent contact repulsion. It is found that adding an attractive resonant odd-wave interaction breaking the rotational symmetry one can make the ground state ferromagnetic. A promising system for the observation of this itinerant ferromagnetic state is a 1D gas of $^{40}$K atoms, where 3D $s$-wave and $p$-wave Feshbach resonances are very close to each other and the 1D confinement significantly reduces the inelastic decay.

cond-mat.quant-gas↗

arXiv2013

Fermi gases in one dimension: From Bethe Ansatz to experiments

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas -- the Gaudin-Yang model -- and its generalisations to multi-component Fermi systems with larger spin symmetries. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.

cond-mat.quant-gas↗

arXiv2012

1D multicomponent Fermions with delta function interaction in strong and weak coupling limits: $κ$-component Fermi gas

We derive the first few terms of the asymptotic expansion of the Fredholm equations for one-dimensional $κ$-component fermions with repulsive and with attractive delta-function interaction in strong and weak coupling regimes. We thus obtain a highly accurate result for the ground state energy of a multicomponent Fermi gas with polarization for these regimes. This result provides a unified description of the ground state properties of the Fermi gas with higher spin symmetries. However, in contrast to the two-component Fermi gas, there does not exist a mapping that can unify the two sets of Fredholm equations as the interacting strength vanishes. Moreover, we find that the local pair correlation functions shed light on the quantum statistic effects of the $κ$-component interacting fermions. For the balanced spin case with repulsive interaction, the ground state energy obtained confirms Yang and You's result [Chin. Phys. Lett. {\bf 28}, 020503 (2011)] that the energy per particle as $κ\to \infty$ is the same as for spinless Bosons.

cond-mat.quant-gas↗

arXiv2012

One-dimensional multicomponent fermions with delta function interaction in strong and weak coupling limits: Two-component Fermi gas

The Fredholm equations for one-dimensional two-component Fermions with repulsive and with attractive delta-function interactions are solved by an asymptotic expansion for A) strong repulsion, B) weak repulsion, C) weak attraction and D) strong attraction. Consequently, we obtain the first few terms of the expansion of ground state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of the Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two sides. Thus the asymptotic expansions of the energies of the repulsive and attractive Fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy analytically connects.

cond-mat.quant-gas↗

arXiv2012

Quantum criticality of a one-dimensional Bose-Fermi mixture

The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study quantum phase diagram, equation of state and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behaviour at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an harmonic trap is also studied within the local density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insights into understanding universal features of many-body critical phenomena.

cond-mat.quant-gas↗