Abstract
A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground-state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take a phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons, supporting trivial and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground-state energy becomes nonanalytical, concurrent with a closing of the band gap, but with no phase transition taking place.
Highlights
Phase transitions are ubiquitous in all branches of physics
There is no change of symmetry or topology across the multicritical line
The present simple model of a topological band insulator defies this notion: The ground-state energy becomes nonanalytical at multicritical lines in the phase diagram, with associated closing of the band gap and divergence of a localization length, and yet there is no change of symmetry or in the topological invariant
Summary
Phase transitions are ubiquitous in all branches of physics. Present-day research has largely focused on equilibrium transitions at zero temperature—quantum phase transitions (QPTs)—identified by the appearance of a nonanalyticity in the ground-state energy of a system in the thermodynamic limit [1]. A QPT is called first order when the first derivative of the ground-state energy with respect to a control parameter (a coupling constant or an external field) becomes discontinuous, or continuous when the discontinuity appears in the second or a higher derivative. These definitions mimic their classical counterparts from equilibrium thermodynamic phase transitions described in terms of a nonanalytical canonical free energy [2]. Wave number (a is the lattice spacing) and φ the phase of the modulation with respect to the underlying lattice This Hamiltonian belongs to the class of generalized Aubry-AndréHarper models [11,12]. Generating a nontrivial topology from a trivial two-band model by increasing the number of bands is an interesting possibility surfaced by the present model
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