We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures.To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement.Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G t t 1 , ( ) in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures.To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement.Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G t t 1 , ( ) in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

arXiv:1410.2226New Journal of PhysicsSep 30, 201522 citations

Theory of a 2D Luttinger liquid

Fedor Vasilievich Kusmartsev, Alan H. Luther, A. A. Nersesyan

Jun 1, 199214 citations

Low temperature dynamics of nonlinear Luttinger liquids

Christoph Karrasch, Rodrigo G. Pereira, Jesko Sirker

We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, $G(t)\sim 1/\sqrt{t},$ in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, $G(t)\sim 1/\sqrt{t},$ in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

Jan 1, 201524 citations

Microscopic Theory of Luttinger Liquids in One Dimension

N. Kawakami, Sung-Kil Yang

Springer series in solid-state sciencesJan 1, 19921 citation

G(t)\sim 1/\sqrt{t},

in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.