Nonequilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions

Abstract

We employ a novel, unbiased renormalization-group approach to investigate nonequilibrium phase transitions in infinite lattice models. This allows us to address the delicate interplay of fluctuations and ordering tendencies in low dimensions out of equilibrium. We study a prototypical model for the metal to insulator transition of spinless interacting fermions coupled to electronic baths and driven out of equilibrium by a longitudinal static electric field. The closed system features a Berezinskii-Kosterlitz-Thouless transition between a metallic and a charge-ordered phase in the equilibrium limit. We compute the nonequilibrium phase diagram and illustrate a highly nonmonotonic dependence of the phase boundary on the strength of the electric field: for small fields, the induced currents destroy the charge order, while at higher electric fields it reemerges due to many-body Wannier-Stark localization physics. Finally, we show that the current in such an interacting nonequilibrium system can counter-intuitively flow opposite to the direction of the electric field. This nonequilibrium steady state is reminiscent of an equilibrium distribution function with an effective negative temperature.

Colloquium: Nonthermal pathways to ultrafast control in quantum materials

“…In a solid-state setting, the crystal lattice can act as a 'thermostat' for the electronic system due to the large timescale separation between electronic and lattice dynamics, with early works suggesting routes towards the controlled dissipative population of singleparticle Floquet states (Dehghani et al, 2014;Iadecola et al, 2015;Seetharam et al, 2015). The phase diagrams of infinite-time steady states of clean systems have been established to exhibit rich phase transitions (Kalthoff et al, 2021;Klöckner et al, 2020;Mendoza-Arenas et al, 2017;Mitra et al, 2006;Peronaci et al, 2018;Walldorf et al, 2019), which are, however, expected to be first order at finite driving frequency (Mathey and Diehl, 2019).…”

Stark many-body localization: Evidence for Hilbert-space shattering

“…It is therefore of interest to numerically investigate the fate of one-dimensional SMBL as reported in Refs. [13,14,22,27,[29][30][31][32][33]. For this purpose we employ the powerful numerical machinery of the time-dependent variational principle (TDVP) [34], a method formulated in terms of the language of matrix product states (MPS).…”

“…This phenomenon was dubbed "negative current" in Ref. [33] and is another sign of non-thermalization.…”

Nonthermal pathways to ultrafast control in quantum materials

“…In a solid-state setting, the crystal lattice can act as a thermostat for the electronic system due to the large time scale separation between electronic and lattice dynamics, with early works suggesting routes towards the controlled dissipative population of singleparticle Floquet states (Dehghani et al, 2014;Iadecola et al, 2015;Seetharam et al, 2015). The phase diagrams of infinite-time steady states of clean systems have been established to exhibit rich phase transitions (Klöckner et al, 2020;Mendoza-Arenas et al, 2017;Mitra et al, 2006;Peronaci et al, 2018;Walldorf et al, 2019), which are, however, expected to be first order at any finite driving frequency (Mathey and Diehl, 2019).…”