Condensed Matter Theory

Abstract:

Studies of random unitary circuits have shown that the calculation of Rényi entropies of entanglement can be mapped to classical statistical mechanics problems in spacetime. In this paper, we develop an analogous spacetime picture of entanglement generation for random free or weakly interacting fermion systems without conservation laws. We first study a free-fermion model, namely a one-dimensional chain of Majorana modes with nearest-neighbor hoppings, random in both space and time. We analyze the $N\mathrm{th}$ Rényi entropy of entanglement using a replica formalism, and we show that the effective model is equivalent to an $\mathrm{SO}\left(2N\right)$ Heisenberg spin chain evolving in imaginary time. By applying a saddle-point approximation to the coherent states path integral for the $N=2$ case, we arrive at a semiclassical picture for the dynamics of the entanglement purity, in terms of two classical fields in spacetime. The classical solutions involve a smooth domain wall that interpolates between two values, with the width of this smooth domain wall spreading diffusively in time. We then study how adding weak interactions to the free-fermion model modifies this spacetime picture. Interactions reduce the symmetry of the effective continuum description. As a result the width of the entanglement domain wall remains finite, rather than growing diffusively in time. This yields a crossover from diffusive to ballistic spreading of information.

Abstract:

SciPost Submission Detail Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

Abstract:

We explore the phase diagrams of moiré materials in search of a class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper [Kwan , .], breaks valley <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>U</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </math> symmetry in a nontrivial fashion wherein the valley order parameter is forced to texture in momentum space as a consequence of band topology. Using detailed Hartree-Fock studies, we establish that the CTI emerges as an energetically competitive intermediate-coupling ground state in several moiré systems that lack a twofold rotation symmetry that forbids the single-particle topology essential to the formation of the CTI valley texture. Published by the American Physical Society 2025