Thermodynamics, spin-charge separation, and correlation functions of spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>fermions with repulsive interaction

Lee, Jen; Guan, Xi‐Wen; Sakai, Kazumitsu; Batchelor, Murray T.

doi:10.1103/physrevb.85.085414

Cited by 17 publications

(34 citation statements)

References 66 publications

(110 reference statements)

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“…For H < 0 the BF phase diagram is identical to that of the FF system with vacuum phase for µ < µ c (H) satisfies (25) for the BF and the FF case as can be derived from the low temperature limit of the TBA equations for the BF case [31] as well as for the FF case [113]. When approaching this line from the polarized phase, its location is again given by the single particle properties of the new admixed particle, the line does not depend on its nature.…”

Section: Boundaries Of the Quantum Critical Regionsmentioning

confidence: 83%

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

Pâţu

Klümper

2019

Phys. Rev. A

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We investigate the one-dimensional mixture of scalar bosons and spin polarized fermions interacting through a δ-function potential. Using a thermodynamic description derived by employing a lattice embedding of the continuum model and the quantum transfer matrix method we perform a detailed analysis of the contact and quantum critical behaviour. We show that the compressibility Wilson ratio presents anomalous enhancement at the quantum critical points and that the boundaries of the quantum critical regions can be well mapped by the maxima of the specific heat. As a function of the coupling strength and temperature the contact presents nonmonotonic behavior. In the strong coupling regime the local minimum exhibited by the contact as a function of temperature is accompanied by a significant momentum reconstruction at both low and high momenta. This momentum reconstruction occurs as the system crosses the boundary between the Tomonaga-Luttinger liquid phase to the spin-incoherent regime and provides an experimental signature of the transition. arXiv:1811.08692v2 [cond-mat.quant-gas]

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Section: Boundaries Of the Quantum Critical Regionsmentioning

confidence: 83%

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

Pâţu

Klümper

2019

Phys. Rev. A

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“…We can see that the equation of state (9) shares a similar form with the one in repulsive SU(2) fermions at the strong coupling limit [21]. The differences are that for the SU(2) fermions the corrections are given by the interaction strength while for this model the corrections are provided by h. The equation of state shows that the low-temperature magnetic susceptibility and specific heat is…”

Section: Low-temperature Equation Of Statementioning

confidence: 89%

“…where F 1/2 (x) is the Fermi-Dirac integral and it can be written in forms of polylog functions [21]. Because the approximation here is given by the small magnetic field and small temperature limit and it requires the relations h T and μ T , the equation of state can not show the quantum criticality.…”

Section: Low-temperature Equation Of Statementioning

confidence: 99%

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Low-temperature properties of an integrable spin-3/2 gas with weak external magnetic field

2013

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We study the low-temperature thermodynamic properties of an integrable spin-3/2 fermionic model. Many interesting kinds of fermionic pairs exist in the systems. By using the Wiener-Hopf method, we obtain the ground state and the equation of state at low temperatures. The ground-state energy without binding energy and Zeeman energy can be represented by the spinless free fermions with an effective mass and a quadratic correction of the weak external magnetic field. We also discuss the quantum criticality for the phase transition from vacuum state to the super Tonks-Girardeau-like phase near the strong coupling limit.

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“…A picture that particles with charge and spin degrees of freedom propagate separately with different velocities has been well-known for 1D electron systems. Their low temperature properties are described by bosonization and Tomonaga-Luttinger liquid theory [48][49][50][51][52][53][54][55][56] , and this phenomenon is known as spin-charge separation [57][58][59][60][61][62][63][64][65][66] , where excitations with charge and spin are called holons and spinons, respectively. A characteristic point of GHD is that this theory is not restricted to low temperature regimes but covers the whole temperature range up to infinity, although it is applicable only to integrable systems.…”

Section: Generalized Hydrodynamic Approach and Partitioning Protocolmentioning

confidence: 99%

Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model

Nozawa,

Tsunetsugu

2019

Preprint

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We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatio-temporal profile of particle density (equivalent to charge density), energy density and their currents using the partitioning protocol; the initial state consists of two semi-infinite different thermal equilibrium states joined at the origin. In this protocol, there appears around the origin a transient region where currents flow, and this region expands its size linearly with time. We examined how density and current profiles depend on initial conditions. Inside the transient region, we have found a clogged region where charge current is zero but nonvanishing energy current flows. This phenomenon is similar to spin-charge separation in Tomonaga-Luttinger liquids, in which spin and charge excitations propagate with different velocities. This region appears when one of the initial states has half-filled electron density, and it is located adjacent to this initial state. We have proved analytically the existence of the clogged region in the infinite temperature case of the half-filled initial state. The existence is confirmed also for finite temperatures by numerical calculations of generalized hydrodynamics. A similar analytical proof is also given for a clogged region of spin current when magnetic field is applied to one and only one of the two initial states. A universal proportionality of charge and spin currents is also proved for a special region, for general initial conditions of electron density and magnetic field. To examine the clogged region of charge current, we have calculated the current contributions of different types of quasiparticles in the Hubbard model. It is found that the charge current component carried by scattering states (i.e. Fermi liquid type) is canceled completely in the clogged region by the counter flows carried by bound-state quasiparticles (called k-Λ strings). Their contributions are not canceled for energy current, which is also proved analytically for special cases, and these different behaviors are the origin of the clogged region. Except for the clogged region, charge and energy densities are in good proportion to each other, and their ratio depends on the initial conditions. This proportionality in nonequilibrium dynamics is reminiscent of Wiedemann-Franz law in thermal equilibrium, which states current proportionality determined by temperature. The long-time stationary values of charge and energy currents were also studied with varying initial conditions. We have compared the results with the values of non-interacting systems and discussed the effects of electron correlations. The ratio of these stationary currents is also analyzed. We have found that the temperature dependence of the ratio is strongly suppressed by electron correlations and even reversed.

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

Cited by 17 publications

References 66 publications

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

Low-temperature properties of an integrable spin-3/2 gas with weak external magnetic field

Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model

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