Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension

TL;DR

This paper investigates a one-dimensional trimer deposition-evaporation model using numerical diagonalization, revealing a new universality class with a specific gap exponent, distinct from known models like KPZ.

Contribution

The study provides the first numerical analysis of the spectral gap in the trimer deposition-evaporation model, identifying a new universality class with a unique gap exponent.

Findings

Gap exponent approximately 2.55 ± 0.15

Model belongs to a new universality class

Spectral gap vanishes as system size increases

Abstract

We study the model of deposition-evaporation of trimers on a line recently introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain with three-spin couplings given by $ H= \sum\displaylimits_i [(1 - \sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+ + h.c]$. We study by exact numerical diagonalization of $H$ the variation of the gap in the eigenvalue spectrum with the system size for rings of size up to 30. For the sector corresponding to the initial condition in which all sites are empty, we find that the gap vanishes as $L^{-z}$ where the gap exponent $z$ is approximately $2.55\pm 0.15$. This model is equivalent to an interfacial roughening model where the dynamical variables at each site are matrices. From our estimate for the gap exponent we conclude that the model belongs to a new universality class, distinct from that studied by Kardar, Parisi and Zhang.