Quantum Phase Transitions beyond the Landau's Paradigm in Sp(4) Spin System

TL;DR

This paper explores unconventional quantum phase transitions in Sp(4) spin systems on different lattices, revealing new critical behaviors beyond traditional Landau theory, with implications for cold atomic systems.

Contribution

It introduces models of quantum phase transitions beyond Landau's paradigm in Sp(4) spin systems, including a fractionalized spin liquid transition and a deconfined critical point.

Findings

Identified a phase transition between spin order and spin liquid with anomalous scaling.

Proposed a deconfined critical point between Neel and VBS orders.

Described critical theories using O(8) sigma and CP(3) models.

Abstract

We propose quantum phase transitions beyond the Landau's paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices, motivated by the exact Sp(4)$\simeq$ SO(5) symmetry of spin-3/2 fermionic cold atomic system with only $s-$wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\times\sqrt{3}$ spin ordered phase and a $Z_2$ spin liquid phase, this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the VBS order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.