Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents

TL;DR

This paper derives universal scaling relations and exact spectral properties for dissipative Tomonaga-Luttinger liquids with SU(N) symmetry, revealing how dissipation affects charge and spin modes differently in non-Hermitian quantum systems.

Contribution

It provides an exact spectrum and critical exponents for dissipative SU(N) Tomonaga-Luttinger liquids using Bethe-ansatz and conformal field theory, extending Haldane's ideal-gas description.

Findings

Spectrum described by charge and spin modes with distinct conformal anomalies

Dissipation affects only the charge mode due to spin-charge separation

Universal scaling relations established for both fermionic and bosonic systems

Abstract

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with 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 SU($N$) symmetry. We uncover that the spectrum of dissipative TL liquids with 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 $N-1$ spin modes characterized by level-$1$ SU($N$) Kac-Moody algebra with the conformal anomaly $c=N-1$, 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 SU($N$) Calogero-Sutherland model with inverse-square long-range interactions.