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Non-equilibrium dynamics of exactly solvable quantum many-body systems
KTH, School of Engineering Sciences (SCI), Physics.ORCID iD: 0000-0003-0011-2937
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: urn:nbn:se:kth:diva-239155ISBN: 978-91-7873-032-2 (print)OAI: oai:DiVA.org:kth-239155DiVA, id: diva2:1263838
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
List of papers
1. Construction by bosonization of a fermion-phonon model
Open this publication in new window or tab >>Construction by bosonization of a fermion-phonon model
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 9, article id 091902Article in journal (Refereed) Published
Abstract [en]

We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization.We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-175654 (URN)10.1063/1.4930299 (DOI)000362569200020 ()2-s2.0-84941912006 (Scopus ID)
Note

QC 20151023

Available from: 2015-10-23 Created: 2015-10-19 Last updated: 2018-11-20Bibliographically approved
2. Steady states and universal conductance in a quenched Luttinger model
Open this publication in new window or tab >>Steady states and universal conductance in a quenched Luttinger model
2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, p. 1-32Article in journal (Refereed) Epub ahead of print
Abstract [en]

We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2016
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-193328 (URN)10.1007/s00220-016-2631-x (DOI)000393599800005 ()2-s2.0-84969822488 (Scopus ID)
Note

QC 20161003

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-11-20Bibliographically approved
3. Time evolution of the Luttinger model with nonuniform temperature profile
Open this publication in new window or tab >>Time evolution of the Luttinger model with nonuniform temperature profile
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
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-211012 (URN)10.1103/PhysRevB.95.235142 (DOI)000404018700002 ()2-s2.0-85024365790 (Scopus ID)
Funder
Swedish Research Council, 2016-05167
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2018-11-20Bibliographically approved
4. Finite-Time Universality in Nonequilibrium CFT
Open this publication in new window or tab >>Finite-Time Universality in Nonequilibrium CFT
2018 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, no 2, p. 353-378Article in journal (Refereed) Published
Abstract [en]

Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

Place, publisher, year, edition, pages
SPRINGER, 2018
Keywords
Nonequilibrium dynamics, Conformal field theory, Heat and charge transport, Luttinger model
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-232397 (URN)10.1007/s10955-018-2025-x (DOI)000437829200004 ()2-s2.0-85044457468 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20180726

Available from: 2018-07-26 Created: 2018-07-26 Last updated: 2018-11-20Bibliographically approved
5. Diffusive Heat Waves in Random Conformal Field Theory
Open this publication in new window or tab >>Diffusive Heat Waves in Random Conformal Field Theory
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a non-trivial real regular contribution that depends on details of the impurities.

National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-239151 (URN)
Note

arXiv:1807.10239 [cond-mat.stat-mech]. QC 20181120

Available from: 2018-11-16 Created: 2018-11-16 Last updated: 2018-11-20Bibliographically approved

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