Relaxation of the order-parameter statistics in the Ising quantum chain

Abstract

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of the 3-states Potts model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we proof that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the n-point spin correlation functions. :1906.00948v1 [cond-mat.stat-mech] Contents arXiv

On the low-energy description for tunnel-coupled one-dimensional Bose gases

“…where the α a,k are defined in (39) and the α s,k in (42). For (46) to be a canonical transformation we require…”

“…An interesting feature of these experiments is that in certain limits, density measurements after matter-wave interference [13,25] correspond to projective von Neumann measurements of the relative phase field [26]. This allows for the reconstruction of full distribution functions of quantum mechanical observables [21][22][23], which is of considerable theoretical interest [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] in general. In the case at hand, situations without tunnel-coupling can be modelled by a two-component Luttinger liquid [45][46][47].…”

Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas

“…Furthermore, we also analytically derive exact expressions for the whole probability distribution of the density operator for any GGE, a quantity also known as Full Counting Statistics (FCS). The FCS of several quantities and in a variety of models have been investigated in several instances [85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100], but for what concerns the LL model only a few results have been obtained so far, despite their relevance in experiments [101][102][103]. For instance, in Ref.…”

Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

“…Being a very natural concept FCS has been studied for a long time in different communities. It has been studied in the context of charge fluctuations 45,46 , Bose gases [47][48][49][50][51] , particle number fluctuations [52][53][54][55][56] , quantum spin chains [57][58][59][60][61][62][63][64] and out of equilibrium quantum systems 51,65,66 .…”