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Time evolution of the Luttinger model with nonuniform temperature profile
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.ORCID iD: 0000-0003-0011-2937
2017 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 23, article id 235142Article in journal (Refereed) Published
Abstract [en]

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 >= 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,T-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.

Place, publisher, year, edition, pages
American Physical Society, 2017. Vol. 95, no 23, article id 235142
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-211012DOI: 10.1103/PhysRevB.95.235142ISI: 000404018700002Scopus ID: 2-s2.0-85024365790OAI: oai:DiVA.org:kth-211012DiVA, id: diva2:1121834
Funder
Swedish Research Council, 2016-05167
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2018-11-20Bibliographically approved
In thesis
1. Non-equilibrium dynamics of exactly solvable quantum many-body systems
Open this publication in new window or tab >>Non-equilibrium dynamics of exactly solvable quantum many-body systems
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium.

In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance.

The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic.

Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2018. p. 94
Series
TRITA-SCI-FOU ; 2018:49
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-239155 (URN)978-91-7873-032-2 (ISBN)
Public defence
2018-12-14, FD5, AlbaNova University Center, KTH Royal Institute of Technology, Stockholm, 10:00
Opponent
Supervisors
Note

QC 20181119

Available from: 2018-11-19 Created: 2018-11-16 Last updated: 2018-11-21Bibliographically approved

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Langmann, EdwinMoosavi, Per

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