Spectral Properties of One-Dimensional Fermi Systems after an Interaction Quench

Abstract

We show that the single-particle spectral properties of gapless one-dimensional Fermi systems in the Luttinger liquid state reached at intermediate times after an abrupt quench of the two-particle interaction are highly indicative of the unusual nonequilibrium nature of this state. The line shapes of the momentum integrated and resolved spectral functions strongly differ from their ground state as well as finite temperature equilibrium counterparts. Using an energy resolution improved version of radio-frequency spectroscopy of quasi one-dimensional cold Fermi gases it should be possible to experimentally identify this nonequilibrium state by its pronounced spectral signatures.PACS numbers: 71.10. Pm, 02.30.Ik, 03.75.Ss, 05.70.Ln Closed one-dimensional (1d) Fermi systems are promising candidates to realize unusual nonequilibrium steady states. In many 1d out of equilibrium systems integrals of motion beyond energy conservation hinder that observables and the reduced density matrix of subsystems relax to values expected for one of the canonical ensembles. Even for generic models, in which those are absent, the restricted phase space available for scattering at least delays thermalization. An intensively studied question is under which conditions 1d systems prepared in the ground state of an initial Hamiltonian H i and brought out of equilibrium by time-evolving them with H f of similar form but with changed parameters eventually thermalize [1][2][3][4][5][6][7][8][9][10][11][12]. Quench protocols of this type can experimentally be realized in cold atomic gases [13, 14]. Increasing theoretical evidence was gathered that in an extended time regime following the after-quench transient one a quasi stationary state exists which does show nonthermal behavior [4, 8, 10, 12,15]. Here we are interested in the properties of this intermediate time steady state regardless if it is the true steady state or if further relaxation sets in on a well separated larger time scale [10]. For nongeneric models which are mappable on free ones the system is stuck in this state for all further times; it can be described by a generalized Gibbs ensemble (GGE) [1,2, 5,[16][17][18][19][20][21]. If the same holds for more complex models which cannot directly be linked to noninteracting ones but are characterized by an infinite set of local conservation laws is heavily investigated [2,[22][23][24][25].Already in equilibrium 1d metals are peculiar. They fall into the Luttinger liquid (LL) universality class which is characterized by power-law decay of correlation functions with interaction dependent exponents [26,27]. The Tomonaga-Luttinger model (TLM), a field theoretical model for which the exact computation of correlation functions is straightforward using bosonization, constitutes the low-energy fixed point model under a renormalization group (RG) procedure of all microscopic models falling into the LL class [26,27]. The power-law decay of the TLM's ground state lesser Green function, with the field operator ψ in the Heisenberg picture, le...

Transport across an impurity in one-dimensional quantum liquids far from equilibrium

“…While this behavior is reminiscent of an effective temperature, we will see that this analogy is only qualitative rather than quantitative, as the scaling of physical quantities in the steady state with respect to this emergent energy scale do not show signature of non-trivial powerlaws like the ones encountered at non-zero temperatures. At the same time we find that deviations from the asymptotic steady state regime, due to transient effects at finite time, display nonequilibrium power laws with characteristic Luttinger liquid exponents which may be a signature of a sort of Luttinger liquid universality out of equilibrium, as recently discussed 29,38,39 . Note that the problem of an impurity in a quenched Luttinger model has been recently addressed in Refs.…”

Long-lived binary tunneling spectrum in the quantum Hall Tomonaga-Luttinger liquid

“…Theoretically the Coulomb interaction between electrons is absorbed under bozonization into noninteracting plasmon modes of collective density excitations [10][11][12]. Therefore, an ideal TL liquid never thermalizes as plasmon excitations are conserved during the transport [13][14][15]. Quantum-Hall edge channels are suitable for demonstrating this nonthermalizing behavior, as they are well isolated from the environment.…”

A Short Review of One-Dimensional Wigner Crystallization

“…The experimental consequences of the Luttinger liquid behavior of fermionic systems can be found in very different contexts, ranging from Bechgaard salts [24,25], to quantum wires [26][27][28][29], quantum Hall edges [30][31][32], quantum spin Hall edges [33,34], and carbon nanotubes [35], even in the presence of mechanical vibrations [36,37]. Interestingly, strongly out of equilibrium scenarios can also be inspected within this framework [38][39][40][41][42][43][44][45][46][47][48][49]. While genuine long range order cannot be established at non-zero temperature, typical correlation lengths exceeding the size of the sample have been conjectured in very diverse contexts [50][51][52][53][54] and are responsible for the so called one-dimensional Wigner molecule.…”