Publications (48)16.47 Total impact
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Article: Universal local pair correlations of Lieb-Liniger bosons at quantum criticality
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ABSTRACT: The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.11/2012; -
Article: Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction
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ABSTRACT: Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics and criticality of one-dimensional spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high precision equation of state from which the Tomonaga-Luttinger liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent $z=2$ and correlation length exponent $\nu=1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger liquid description.01/2012; -
Article: Quantum criticality of spin-1 bosons in a 1D harmonic trap
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ABSTRACT: We investigate universal thermodynamics and quantum criticality of spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions in a one-dimensional harmonic trap. From the equation of state, we find that a partially-polarized core is surrounded by two wings composed of either spin-singlet pairs or a fully spin-aligned Tonks-Girardeau gas depending on the polarization. We describe how the scaling behaviour of density profiles can reveal the universal nature of quantum criticality and map out the quantum phase diagram. We further show that at quantum criticality the dynamical critical exponent $z = 2$ and correlation length exponent $\nu=1/2$. This reveals a subtle resemblance to the physics of the spin-1/2 attractive Fermi gas.11/2011; -
Article: The asymptotic Bethe ansatz solution for one-dimensional SU(2) spinor bosons with finite range Gaussian interactions
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ABSTRACT: We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a two-body finite range Gaussian interaction potential. We show that the model is exactly solvable when the width of the interaction potential is much smaller compared to the inter-particle separation. This model is then solved via the asymptotic Bethe ansatz technique. The ferromagnetic ground state energy and chemical potential are derived analytically. We also investigate the effects of a finite range potential on the density profiles through local density approximation. Finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials.06/2011; -
Article: Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction
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ABSTRACT: We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ll 1$ and for a magnetic field close to the critical field $H\rightarrow H_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.04/2011; -
Article: Exactly solvable models and ultracold Fermi gases
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ABSTRACT: Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Journal of Statistical Mechanics Theory and Experiment 12/2010; 2010(12):P12014. · 1.73 Impact Factor -
Article: Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
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ABSTRACT: Using Yang and Yang's particle-hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general $SU(\kappa)$ fermionic system in one-dimension for both the repulsive and attractive regimes under the presence of an external magnetic field. These equations are derived from Sutherland's Bethe ansatz equations by using the spin-string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground state energies for both strongly repulsive and strongly attractive regimes.10/2010; -
Article: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
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ABSTRACT: We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang-Yang) equation. The expression for the equation of state allows the exploration of Tomonaga-Luttinger liquid physics and quantum criticality in an archetypical quantum system. In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility. It has been shown recently by Guan and Ho (arXiv:1010.1301) that such scaling can be used to map out the criticality of ultracold fermionic atoms in experiments. We show here how to map out quantum criticality for Lieb-Liniger bosons. More generally the polylog function formalism can be applied to a wide range of Bethe ansatz integrable quantum many-body systems which are currently of theoretical and experimental interest, such as strongly interacting multi-component fermions, spinor bosons and mixtures of bosons and fermions.10/2010; -
Article: Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms
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ABSTRACT: A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance. Comment: 12 pages, 3 figures12/2009; -
Article: Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin exchange interaction
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ABSTRACT: We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field $H$ is less than the lower critical field $H_{c1}$; (ii) a ferromagnetic phase of atoms in the hyperfine state $|F=1, m_{F}=1>$ when the external magnetic field exceeds the upper critical field $H_{c2}$; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region $H_{c1}<H<H_{c2}$. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired $m_{F}=1$ bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime. Comment: 21 pages, 3 figures09/2009; -
Article: Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions
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ABSTRACT: Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory. Comment: 13 pages, 4 figures04/2009; -
Article: Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization
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ABSTRACT: An extensive investigation is given for magnetic properties and phase transitions in one-dimensional Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in one-dimensional interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime. Comment: 21 pages, 7 figures, some clarifications added, with some new and updated references03/2009; -
Article: Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
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ABSTRACT: We investigate magnetic properties and statistical effects in 1D strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization and susceptibility in the presence of an external magnetic field $H$ are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value $H^F_c\approx \frac{8}{\gamma}E_F$, where $E_F$ is the Fermi energy and $\gamma$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0 and the critical value $H=H^M_c\approx \frac{16}{\gamma}E_F$. We find that a pure boson phase occurs in the absence of the external field, fully-polarized fermions and bosons coexist for $0<H<H^M_c$, and a fully-polarized fermion phase occurs for $H\ge H_c^M$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.07/2008; -
Article: Magnetic phase transitions in one-dimensional strongly attractive three-component ultracold fermions.
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ABSTRACT: We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.Physical Review Letters 05/2008; 100(20):200401. · 7.37 Impact Factor -
Article: One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
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ABSTRACT: We propose an exactly solvable model of one-dimensional anyons with competing $\delta$-function and derivative $\delta$-function interaction potentials. The Bethe ansatz equations are derived in terms of the $N$-particle sector for the quantum anyonic field model of the generalized derivative nonlinear Schr\"{o}dinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of $\delta$-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles. Comment: 9 pages, 2 figures, minor changes, references updated05/2008; -
Article: Ferromagnetic behaviour in the strongly interacting two-component Bose gas
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ABSTRACT: We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat $c_v \sim T^{1/2}$ and the susceptibility $\chi \sim T^{-2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.08/2007; -
Article: Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
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ABSTRACT: We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H < H_{c1}$. A completely ferromagnetic phase without pairing occurs when the external field $H > H_{c2}$. In the region $H_{c1} < H < H_{c2}$ we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.03/2007; -
Article: Bethe Ansatz for 1D interacting anyons
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ABSTRACT: This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The thermodynamic Bethe Ansatz equations defining the temperature dependent properties of the model are also derived, from which some groundstate properties are obtained.12/2006; -
Article: Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas
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ABSTRACT: We discuss recent results on the relation between the strongly interacting one-dimensional Bose gas and a gas of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include the statistical profiles, the specific heat and local pair correlations. In the strong coupling limit $\gamma \to \infty$, the Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation from Fermi statistics during boson fermionization for finite but large interaction strength $\gamma$ is described by the relation $\alpha \approx 1 - 2/\gamma$, where $\alpha$ is a measure of the GES. This gives a quantitative description of the fermionization process. In this sense the recent experimental measurement of local pair correlations in a 1D Bose gas of $^{87}$Rb atoms also provides a measure of the deviation of the GES parameter $\alpha$ away from the pure Fermi statistics value $\alpha=1$. Other thermodynamic properties, such as the distribution profiles and the specific heat, are also sensitive to the statistics. They also thus provide a way of exploring fractional statistics in the strongly interacting 1D Bose gas.09/2006; -
Article: Generalized exclusion statistics and degenerate signature of strongly interacting anyons
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ABSTRACT: We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.07/2006;
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Institutions
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2003–2011
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Australian National University
- Department of Theoretical Physics
Canberra, Australian Capital Territory, Australia
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