Time evolution of the Luttinger model with nonuniform temperature profile

Abstract

We study the time evolution of a one-dimensional interacting fermion system described by the Luttinger model starting from a nonequilibrium state defined by a smooth temperature profile $T(x)$. As a specific example we consider the case when $T(x)$ is equal to $T_L$ ($T_R$) far to the left (right). Using a series expansion in $\epsilon =2(T_R-T_L)/(T_L+T_R)$, we compute the energy density, the heat current density, and the fermion two-point correlation function for all times $t\ge 0$. For local (delta-function) interactions, the first two are computed to all orders, giving simple exact expressions involving the Schwarzian derivative of the integral of $T(x)$. For nonlocal interactions, breaking scale invariance, we compute the nonequilibrium steady state (NESS) to all orders and the evolution to first order in $\epsilon$. The heat current in the NESS is universal even when conformal invariance is broken by the interactions, and its dependence on $T_{L,R}$ agrees with numerical results for the $XXZ$ spin chain. Moreover, our analytical formulas predict peaks at short times in the transition region between different temperatures and show dispersion effects that, even if nonuniversal, are qualitatively similar to ones observed in numerical simulations for related models, such as spin chains and interacting lattice fermions.

9 pages, REVTeX, 4 figures; extended version of original submission with minor corrections; final published version with minor updates

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Heat Transport in low-dimensional systems
• Experimental Observation of a Generalized Gibbs Ensemble
• The Luttinger model following a sudden interaction switch-on
• Quantum quench dynamics of the Luttinger model
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Luttinger liquid universality in the time evolution after an interaction quench
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Energy transport in stochastically perturbed lattice dynamics
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Quantum Quench for inhomogeneous states in the non-local Luttinger model

Cited by in corpus (26)

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• Solvable Hydrodynamics of Quantum Integrable Systems
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• Dynamics of hard rods with initial domain wall state
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Geometric approach to inhomogeneous Floquet systems
• Finite-time universality in nonequilibrium CFT
• Inhomogeneous conformal field theory out of equilibrium
• Diffusive Heat Waves in Random Conformal Field Theory
• Non-equilibrium quantum transport in presence of a defect: the non-interacting case
• Kinetic theory of quantum and classical Toda lattices
• Linearized regime of the generalized hydrodynamics with diffusion
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Anyon Quantum Transport and Noise away from Equilibrium
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Full counting statistics of energy transfers in inhomogeneous nonequilibrium states of (1+1)D CFT
• Emergence of generalized hydrodynamics in the non-local Luttinger model
• Non-equilibrium field theory with a temperature gradient: Thermal current in a nanowire
• Self-equilibration theorem in quantum-point contacts of interacting electrons: time-dependent quantum fluctuations of tunnel transport beyond the Levitov-Lesovik scattering approach
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Perfect Wave Transfer in Continuous Quantum Systems
• Temperature inhomogeneity in non-equilibrium field theory for electrons in a nanowire: thermodynamic and transport properties
• Electrostatic solution of massless quenches in Luttinger liquids
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation
• Non-integrable fermionic chains near criticality