Universal description of dissipative Tomonaga-Luttinger liquids with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> spin symmetry: Exact spectrum and critical exponents
Kazuki Yamamoto, Norio Kawakami
Abstract
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.