Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain

Abstract

We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems. Our analytic calculation is based on effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the massless regime with weak dissipation belongs to the universality class characterized by the complex-valued TL parameter, which is related to the complex generalization of the c = 1 conformal field theory. As the dissipation strength increases, the values of the TL parameter obtained by the NH-DMRG begin to deviate from those obtained by the Bethe-ansatz analysis, indicating that the model becomes massive for strong dissipation. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.

PT -symmetric, non-Hermitian quantum many-body physics—a methodological perspective

“…However, others employ the alternative ones described in the present subsection [49,56,58,[89][90][91][92][93]. Some even present results for expectation values of observables obtained by both definitions in a single paper [78,79,81,84,94]. One of the central goals of this review is to contribute to a resolution of this conflict.…”

“…For these reasons the above definitions are used in mathematical physics [9,23] and non-Hermitian quantum field theory [9,[71][72][73][74][75]. They have also been adopted by parts of the condensed matter community to study quantum many-body systems [76][77][78][79][80][81][82][83][84] and non-Hermitian topological systems [10,11,85,86]. 17 However, the above postulates of a PT -symmetric observable and of a PT -symmetric 'expectation value' have limiting weaknesses which cannot be ignored.…”

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

“…non-Hermitian models have initially focused on single-particle models [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80], and its extension to the fully interacting realm has also gained attention recently [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97]. Aside from these case studies, unraveling the physics of interacting non-Hermitian systems remains an open challenge due to the scarcity of exactly solvable models, and as conventional (Hermitian) many-body methods cannot be directly applied to the non-Hermitian limit.…”

Weakly interacting Bose gas with two-body losses

“…Recently, with the development of theoretical and experimental methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], much more attention has been paid to behaviors of cold atom systems with dissipation. For bosonic and fermionic models, single particle and two-body dissipation processes such as particle pump and loss can be realized [30][31][32][33][34][35][36].…”