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Physical review. B, Condensed matter

Roughening transition in quantum interfaces

Eduardo Fradkin

Published Nov 1, 1983• 44 citations
Publisher

Abstract

The roughening transition in interfaces of quantum crystals and spin systems is studied. Quantum-mechanical solid-on-solid-like models are presented. I show that quantum interfaces of three-dimensional systems are generally smooth at zero temperature and display a classical roughening transition. In two dimensions, systems with discrete symmetry display a roughening transition at zero temperature.

DOI
10.1103/physrevb.28.5338

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The roughening transition in interfaces of quantum crystals and spin systems is studied. Quantum-mechanical solid-on-solid-like models are presented. I show that quantum interfaces of three-dimensional systems are generally smooth at zero temperature and display a classical roughening transition. In two dimensions, systems with discrete symmetry display a roughening transition at zero temperature.
We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕21∕21∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional U(1)\mathrm{U}(1)U(1) universality class and the interface remains smooth. Similar phenomena are expected for domain walls in quantum antiferromagnets.
Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a gapped bulk. In this work, we present the first tensor-network study of the paradigmatic interface roughening transition of the 3-D Ising model using highly asymmetric lattices that are infinite in the (xy)(xy)(xy) direction and finite in zzz. By reducing the problem to an effective 2-D tensor network, we study how truncating the zzz direction reshapes the physics of the interface. For a truncation based on open boundary conditions, we demonstrate that varying the interface width gives rise to either a Z2\mathbb{Z}_2Z2​ symmetry breaking transition (for odd LzL_zLz​) or a smooth crossover(for even LzL_zLz​). For antiperiodic boundary conditions, we obtain an effective Zq\mathbb{Z}_qZq​ clock model description with q=2Lzq=2L_zq=2Lz​ that exhibits an intermediate Luttinger liquid phase with an emergent $\U(1)$ symmetry.
The properties of interfaces are key to understanding the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale tree tensor network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.
We study the roughening transition of the dual of the two-dimensional (2D) XY model, of the discrete Gaussian model, of the absolute value solid-on-solid model and of the interface in an Ising model on a three-dimensional (3D) simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body-centred solid-on-solid (BCSOS) model. Our estimates for the critical couplings are , and for the XY model, the discrete Gaussian model and the absolute value solid-on-solid model, respectively. For the inverse roughening temperature of the Ising interface we find . To the best of our knowledge, these are the most precise estimates for these parameters published so far.
The zero-temperature triangular Ising antiferromagnet is mapped onto a solid-on-solid (SOS) model. The system undergoes a roughening transition characterised by a critical exponent alpha = 1 / 2 , by the absence of excitations in the smooth phase, and by domain wall excitations (stripes) in the rough phase. At infinite SOS temperature the height-height correlation function is explicitly calculated with the aid of known four-point Ising correlations. The authors point out that a certain six-vertex model with a comparable SOS interpretation has an identical critical temperature, critical exponent and critical amplitude. This is in support of existing ideas on university in systems with striped phases.