[Paper Review] Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase

Bin-Bin Chen, Xu Zhang+3 more|arXiv (Cornell University)|Jul 11, 2023

Physics of Superconductivity and Magnetism9 citations

TL;DR

The paper uses spherical Landau level regularization of the (2+1)D SO(5) NLSM with a topological term to map out its phase diagram, identifying Néel, VBS, FM, VP phases, a gapless disordered region, and a multicritical point.

ABSTRACT

Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Here we apply the spherical Landau level regularization upon the exact (2+1)D SO(5) non-linear sigma model with a topological term to study the potential DQCP therein. We perform density matrix renormalization group (DMRG) simulation with SU(2)$_\mathrm{spin} imes$U(1)$_\mathrm{charge} imes$U(1)$_\mathrm{angular-momentum}$ symmetries explicitly implemented. Using crossing point analysis for the critical properties of the DMRG data, accompanied by quantum Monte Carlo simulations, we accurately obtain the comprehensive phase diagram of the model and find various novel quantum phases, including Néel, ferromagnet (FM), valence bond solid (VBS), valley polarized (VP) states and a gapless quantum disordered phase occupying extended area of the phase diagram. The VBS-Disorder and Néel-Disorder transitions are continuous with non-Wilson-Fisher exponents. Our results show the VBS and Néel states are separated by either a weakly first-order transition or the disordered region with a multicritical point in between, thus opening up more interesting questions on the two-decade long debate on the nature of DQCP.

Motivation & Objective

• Motivate beyond-LGW criticality via the SO(5) DQCP framework and explore lattice realizations.
• Map the full phase diagram across SO(5) symmetric and symmetry-broken regimes.
• Identify continuous and first-order transitions, including a multicritical point separating VBS/Néel and disordered regions.
• Characterize the disordered phase as gapless and its relation to symmetry-enforced gaplessness.

Proposed method

• Apply spherical Landau level regularization to the (2+1)D SO(5) NLSM with a WZW term.
• Perform DMRG with explicit SU(2)spin×U(1)charge×U(1) angular-momentum symmetries.
• Use ED and QMC as complementary methods.
• Implement crossing point analysis on DMRG data to extract critical points and exponents.
• Analyze order parameters from fermion bilinears and SO(5) generators to identify phases.
• Explore system sizes up to N=16 on the sphere and finite-size scaling behaviors.

Experimental results

Research questions

• RQ1 What is the full phase diagram of the (2+1)D SO(5) NLSM with a topological term on a sphere when moving away from the SO(5) symmetric line?
• RQ2 Do continuous VBS-Disorder and Néel-Disorder transitions occur, and what are their critical exponents?
• RQ3 Is there a gapless disordered region separating VBS and Néel phases, and where is the multicritical point located?
• RQ4 How does SO(5) symmetry breaking impact the nature of transitions between Néel, VBS, FM, and VP phases?

Key findings

• The phase diagram contains Néel, VBS, FM, and VP phases plus a disorder phase.
• A gapless disordered region separates the VBS and Néel states.
• VBS-Disorder and Néel-Disorder transitions are continuous with non-Wilson-Fisher exponents.
• A multicritical point exists where the VBS-Disorder and Néel-Disorder boundaries meet along the SO(5) line.
• Along negative SO(5) lines, FM and VP phases emerge via first-order transitions.
• Along the SO(5) line near the multicritical point, a first-order boundary spontaneously breaks SO(5).