Vaporization Dynamics of a Dissipative Quantum Liquid

Abstract

We study the heating dynamics of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The fermionic single particle density matrix, and many other correlators, retain the initial Luttinger liquid correlations in space but decay exponentially in time with a rate that depends on the strength of the interaction. The spectrum of the time evolved density matrix is gapped, which collapses gradually as − ln(t). The von Neumann entropy crosses over from the early time −t ln(t) behaviour to a ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results establish the validity of bosonization for the early time dynamics of 1D lattice models, and could be observed experimentally in bosonic Luttinger liquids.

Dissipative dynamics in the free massive boson limit of the sine-Gordon model

“…The linear growth of the boson number implies that in the long time limit the system is heated up to infinite temperature. This feature is the same as found in the gapless Luttinger model [27,45], and follows from the fact that the jump operator is hermitian.…”

“…and determine the functions F RR (x, t) and F LR (x, t). In contrast to the dissipative Luttinger liquid case [27], the correlator between right and left moving fermions becomes finite due to the presence of the gap. We find that in the long distance and long time limit, the single particle density matrices of both G RR and G LR decay exponentially with an exponent proportional to −γ t |x| ∆ 2 where γ and ∆ are the dissipative coupling and the gap, respectively.…”

“…Here, ω(q) = (v 0 + g 4 )q + ∆ 2 /(2v 0 q) and g(q) = g 2 q + ∆ 2 /(2v 0 q) with v 0 the bare sound velocity of the non-interacting and non-gapped system, g 2 and g 4 are the conventional forward scattering interactions [8,38] and the energy scale ∆ ∼ 2J is proportional to the gap or mass of the elementary excitations. Note that in the absence of ∆, the model is identical to the interacting Luttinger model [27].…”

“…In Eq. ( 7) j(x) is the current operator, which is a natural choice of jump operator when the environment is a fluctuating vector potential or gauge field [12,27,[39][40][41][42]. These naturally couple to local currents.…”

“…The interplay of dissipation and strong correlations, combined with reduced dimensionality [9][10][11][12][13][14][15][16][17][18], promises to provide a plethora of interesting phenomena [19][20][21][22][23][24][25][26]. This includes algebraic or exponential decay of correlation function in dissipative many-particle systems [10], universal features in the vaporization dynamics of Luttinger liquids [27] or targeted cooling into topological states from arbitrary initial states [19,26]. In addition, propagators and correlation spreading also reveal unexpected features [14].…”