Field-induced superfluids and Bose liquids in Projected Entangled Pair States

TL;DR

This paper explores how magnetic field-induced doping in two-dimensional quantum spin liquids affects superfluid and Bose liquid states, using PEPS framework to analyze various lattice models and their topological properties.

Contribution

It provides a comprehensive PEPS-based analysis of doping effects on superfluid and Bose liquids in different lattice geometries, highlighting topological and entanglement changes.

Findings

Doping induces Bose condensation with magnetic order on honeycomb lattice.

Doping preserves U(1) symmetry but destroys Z_2 topological order in RVB states.

Longer-range interactions emerge in entanglement Hamiltonian upon doping.

Abstract

In two-dimensional incompressible quantum spin liquids, a large enough magnetic field generically induces "doping" of polarized S=1 triplons or S=1/2 spinons. We review a number of cases such as spin-3/2 AKLT or spin-1/2 Resonating Valence Bond (RVB) liquids where the Projected Entangled Pair States (PEPS) framework provides very simple and comprehensive pictures. On the bipartite honeycomb lattice, simple PEPS can describe Bose condensed triplons (AKLT) or spinons (RVB) superfluids with transverse staggered (N\'eel) magnetic order. On the Kagome lattice, doping the RVB state with deconfined spinons or triplons (i.e. spinon bound pairs) yields uncondensed Bose liquids preserving U(1) spin-rotation symmetry. We find that spinon (triplon) doping destroys (preserves) the topological Z_2 symmetry of the underlying RVB state. We also find that spinon doping induces longer range interactions in the entanglement Hamiltonian, suggesting the emergence of (additive) log-corrections to the entanglement entropy.