Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1104.2352 · Physical Review B

Thermodynamics, spin-charge separation, and correlation functions of spin- 1/2 fermions with repulsive interaction

J. Y. Lee, Xin Guan, Kazumitsu Sakai, Murray T. Batchelor

Published Feb 8, 2012• 19 citations
arXivHTMLPDF

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 $\text{SU}(2)$ 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 $H\ensuremath{\ll}1$ and for a magnetic field close to the critical field $H\ensuremath{\rightarrow}{H}_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.

DOI
10.1103/physrevb.85.085414

Related papers

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions

Peng He, Jen Yee Lee, Xi‐Wen Guan +2 more

The low temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener-Hopf method. It is shown 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(3) Heisenberg spin chain. Beyond the Tomonaga-Luttinger liquid regime, the equation of state is given in terms of the polylog function for a weak external field. The results obtained are essential for further study of quantum criticality in strongly repulsive three-component fermions.

arXiv:1105.1570•Journal of Physics A Mathematical and Theoretical•Sep 15, 2011•4 citations

Universal low-energy physics in 1D strongly repulsive multi-component Fermi gases

Yuzhu Jiang, Peng He, Xi‐Wen Guan

Abstract It has been shown (Yang and You 2011 Chin. Phys. Lett. 28 020503 ) 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 . This behavior was experimentally evidenced through quasi-1D tightly trapping ultracold 173 Yb atoms in a recent paper (Pagano et al 2014 Nat. Phys. 10 198 ). However, understanding of low-temperature behavior of Fermi gases with a repulsive interaction requires 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 temperature 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 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 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 behavior of physical quantities at finite temperature are analytically derived in terms of the polylogarithm functions in the quantum critical region.

arXiv:1602.02507•Journal of Physics A Mathematical and Theoretical•Mar 18, 2016•7 citations

Exact results of one-dimensional repulsive Hubbard model

Jiajia Luo, Han Pu, Xi‐Wen Guan

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.

arXiv:2307.00890•Jul 3, 2023•0 citations

Emergence and Disruption of Spin-Charge Separation in One-Dimensional Repulsive Fermions

Feng He, Yuzhu Jiang, Hai‐Qing Lin +3 more

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 that 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.

arXiv:2004.12637•Physical Review Letters•Nov 2, 2020•22 citations

Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

C. C. N. Kuhn, Xin Guan, Angela Foerster +1 more

Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics, and criticality of one-dimensional (1D) 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 $\ensuremath{\nu}=1/2$ 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.

arXiv:1201.6456•Physical Review A•Apr 9, 2012•9 citations

Thermodynamics and correlation functions of integrable models in one-dimension

Jen Yee Lee

In this thesis, we investigate thermodynamic properties, magnetic phase transitions and correlation functions of integrable quantum many-body systems in the field of ultracold atomic gases. The scope of our investigation encompasses three models in one-dimension that are integrable by means of the Bethe ansatz method. They are the multi-component 5-interacting Fermi gas, the spin-l Bose gas with antiferromagnetic spin interaction and the SU(2) spinor Bose gas with finite-range Gaussian interaction. We derive the thermodynamic Bethe ansatz equations for the general SU(k) Fermi gas. We illustrate the root patterns and give a quantitative description of the ground state properties for the strongly and weakly interacting regimes. The thermodynamics and magnetic phase transitions are described quantitatively by means of the thermodynamic Bethe ansatz equations. We find that all phase transitions in the attractive regime are of second order with a linear field dependent magnetization in the vicinities of critical points. The SU(2) Fermi gas is studied in more detail. The low temperature thermodynamics for the repulsive case is derived by means of the Wiener-Hopf technique. Finite-size corrections and correlation functions for both the repulsive and attractive cases are derived from the nested Bethe ansatz equations and conformal field theory. In the attractive case, we show that spatial oscillations of the leading terms in the pair correlation function and spin correlation function solely depend on the mismatch between Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristic of a Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) state. For the spin-l Bose gas with antiferromagnetic spin interaction, we find that at zero temperature, the system exhibits three quantum phases: a phase with singlet pairs of bosons, a fully-polarized Tonks-Girardeau gas phase of unpaired ms = 1 bosons, and a mixed phase of singlet pairs and unpaired ms = 1 bosons. Phase transitions in the vicinities of the critical fields are also of second order with a linear field dependent magnetization. Finally, we use the asymptotic Bethe ansatz method to derive the quasimomenta distribution and ground state energy for the SU(2) spinor Bose gas with finite-range Gaussian interaction. We show that finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials by studying the spatial density profiles as the interaction width increases.

•Jan 1, 2011•0 citations
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)\text{SU}(2)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\ensuremath≪1H\ensuremath{\ll}1H\ensuremath≪1 and for a magnetic field close to the critical field H\ensuremath→HcH\ensuremath{\rightarrow}{H}_{c}H\ensuremath→Hc​. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.
The low temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener-Hopf method. It is shown 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(3) Heisenberg spin chain. Beyond the Tomonaga-Luttinger liquid regime, the equation of state is given in terms of the polylog function for a weak external field. The results obtained are essential for further study of quantum criticality in strongly repulsive three-component fermions.
Abstract It has been shown (Yang and You 2011 Chin. Phys. Lett. 28 020503 ) 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 . This behavior was experimentally evidenced through quasi-1D tightly trapping ultracold 173 Yb atoms in a recent paper (Pagano et al 2014 Nat. Phys. 10 198 ). However, understanding of low-temperature behavior of Fermi gases with a repulsive interaction requires 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 temperature 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 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 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 behavior of physical quantities at finite temperature are analytically derived in terms of the polylogarithm functions in the quantum critical region.
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.
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 that 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.
Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics, and criticality of one-dimensional (1D) 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=2z=2z=2 and correlation length exponent $\ensuremath{\nu}=1/2$ 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.
In this thesis, we investigate thermodynamic properties, magnetic phase transitions and correlation functions of integrable quantum many-body systems in the field of ultracold atomic gases. The scope of our investigation encompasses three models in one-dimension that are integrable by means of the Bethe ansatz method. They are the multi-component 5-interacting Fermi gas, the spin-l Bose gas with antiferromagnetic spin interaction and the SU(2) spinor Bose gas with finite-range Gaussian interaction. We derive the thermodynamic Bethe ansatz equations for the general SU(k) Fermi gas. We illustrate the root patterns and give a quantitative description of the ground state properties for the strongly and weakly interacting regimes. The thermodynamics and magnetic phase transitions are described quantitatively by means of the thermodynamic Bethe ansatz equations. We find that all phase transitions in the attractive regime are of second order with a linear field dependent magnetization in the vicinities of critical points. The SU(2) Fermi gas is studied in more detail. The low temperature thermodynamics for the repulsive case is derived by means of the Wiener-Hopf technique. Finite-size corrections and correlation functions for both the repulsive and attractive cases are derived from the nested Bethe ansatz equations and conformal field theory. In the attractive case, we show that spatial oscillations of the leading terms in the pair correlation function and spin correlation function solely depend on the mismatch between Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristic of a Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) state. For the spin-l Bose gas with antiferromagnetic spin interaction, we find that at zero temperature, the system exhibits three quantum phases: a phase with singlet pairs of bosons, a fully-polarized Tonks-Girardeau gas phase of unpaired ms = 1 bosons, and a mixed phase of singlet pairs and unpaired ms = 1 bosons. Phase transitions in the vicinities of the critical fields are also of second order with a linear field dependent magnetization. Finally, we use the asymptotic Bethe ansatz method to derive the quasimomenta distribution and ground state energy for the SU(2) spinor Bose gas with finite-range Gaussian interaction. We show that finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials by studying the spatial density profiles as the interaction width increases.