65 research outputs found
Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
One of the most straightforward ways to study thermal properties beyond linear
response is to monitor the relaxation of an arbitrarily large left-right
temperature gradient TL−TR. In one-dimensional systems which support ballistic
thermal transport, the local energy currents ⟨j(t)⟩ acquire a nonzero value at
long times, and it was recently investigated whether or not this steady state
fulfills a simple additive relation ⟨j(t→∞)⟩=f(TL)−f(TR) in integrable models.
In this paper, we probe the nonequilibrium dynamics of the Hubbard chain using
density matrix renormalization group (DMRG) numerics. We show that the above
form provides an effective description of thermal transport in this model;
violations are below the finite-time accuracy of the DMRG. As a second setup,
we study how an initially equilibrated system radiates into different
nonthermal states (such as the vacuum)
Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
We illustrate how finite-temperature charge and thermal Drude weights of one-
dimensional systems can be obtained from the relaxation of initial states
featuring global (left–right) gradients in the chemical potential or
temperature. The approach is tested for spinless interacting fermions as well
as for the Fermi-Hubbard model, and the behavior in the vicinity of special
points (such as half filling or isotropic chains) is discussed.We present
technical details on how to implement the calculation in practice using the
density matrix renormalization group and show that the non-equilibrium
dynamics is often less demanding to simulate numerically and features simpler
finite-time transients than the corresponding linear response current
correlators; thus, new parameter regimes can become accessible. As an
application, we determine the thermal Drude weight of the Hubbard model for
temperatures T which are an order of magnitude smaller than those reached in
the equilibrium approach. This allows us to demonstrate that at low T and half
filling, thermal transport is successively governed by spin excitations and
described quantitatively by the Bethe ansatz Drude weight of the Heisenberg
chain
Expansion potentials for exact far-from-equilibrium spreading of particles and energy
The rates at which energy and particle densities move to equalize arbitrarily
large temperature and chemical potential differences in an isolated quantum
system have an emergent thermodynamical description whenever energy or particle
current commutes with the Hamiltonian. Concrete examples include the energy
current in the 1D spinless fermion model with nearest-neighbor interactions
(XXZ spin chain), energy current in Lorentz-invariant theories or particle
current in interacting Bose gases in arbitrary dimension. Even far from
equilibrium, these rates are controlled by state functions, which we call
``expansion potentials'', expressed as integrals of equilibrium Drude weights.
This relation between nonequilibrium quantities and linear response implies
non-equilibrium Maxwell relations for the Drude weights. We verify our results
via DMRG calculations for the XXZ chain.Comment: v2: to appear in PR
Second order functional renormalization group approach to one-dimensional systems in real and momentum space
We devise a functional renormalization group treatment for a chain of
interacting spinless fermions which is correct up to second order in
interaction strength. We treat both inhomogeneous systems in real space as
well as the translationally invariant case in a k-space formalism. The
strengths and shortcomings of the different schemes as well as technical
details of their implementation are discussed. We use the method to study two
proof-of-principle problems in the realm of Luttinger liquid physics, namely,
reflection at interfaces and power laws in the occupation number as a function
of crystal momentum
Functional renormalization-group approach
We present a functional renormalization-group approach to interacting topological Green's function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green's function. Our results for the phase boundary are quantitatively benchmarked against density matrix renormalization-group data
Solvable Hydrodynamics of Quantum Integrable Systems
The conventional theory of hydrodynamics describes the evolution in time of
chaotic many-particle systems from local to global equilibrium. In a quantum
integrable system, local equilibrium is characterized by a local generalized
Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study
time evolution from local equilibria in such models by solving a certain
kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local
pseudo-momentum density. Explicit comparison with density matrix
renormalization group time evolution of a thermal expansion in the XXZ model
shows that hydrodynamical predictions from smooth initial conditions can be
remarkably accurate, even for small system sizes. Solutions are also obtained
in the Lieb-Liniger model for free expansion into vacuum and collisions between
clouds of particles, which model experiments on ultracold one-dimensional Bose
gases.Comment: 6+5 pages, published versio
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