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

和樹 山本, Kazuki Yamamoto, Norio Kawakami

L.S. Lima

G. Jüttner, A. Klümper, J. Suzuki

Kazuki Yamamoto, Masaya Nakagawa, Masaki Tezuka +2 more

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.

Kazuki Yamamoto, Norio Kawakami

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with $\mathrm{SU}(N$) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with $\mathrm{SU}(N$) symmetry. We uncover that the spectrum of dissipative TL liquids with $\mathrm{SU}(N$) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of $c=1$ U(1) Gaussian CFT, and $N\ensuremath{-}1$ spin modes characterized by level-$1\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N$) Kac-Moody algebra with the conformal anomaly $c=N\ensuremath{-}1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the $\mathrm{SU}(N$) Calogero-Sutherland model with inverse-square long-range interactions.

Boqiang Li, Xun Chen, Yuqian Zhao +3 more

The spin-$1/2$ ferromagnetic XXZ chain is a prototypical many-body quantum model, exactly solvable via the integrable Bethe ansatz method, hosting a Tomonaga-Luttinger spin liquid. However, its clear experimental realizations remain absent. Here, we present a thorough investigation of the magnetism of the structurally disorder-free compound $\mathrm{LuCu}{(\mathrm{OH})}_{3}{\mathrm{SO}}_{4}$. By conducting magnetization and electron-spin-resonance measurements on the single-crystal sample, we establish that the title compound approximates the spin-$1/2$ ferromagnetic XXZ chain model with a nearest-neighbor exchange strength of ${J}_{1}\ensuremath{\sim}65\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and an easy-plane anisotropy of $\ensuremath{\sim}0.994$. The specific heat demonstrates a distinctive power-law behavior at low magnetic fields (with energy scales $\ensuremath{\le}0.02{J}_{1}$) and low temperatures $(T\ensuremath{\le}0.03{J}_{1})$. This behavior is consistent with the expectations of the ideal spin-$1/2$ ferromagnetic XXZ chain model, thereby supporting the formation of a gapless Tomonaga-Luttinger spin liquid in $\mathrm{LuCu}{(\mathrm{OH})}_{3}{\mathrm{SO}}_{4}$.