First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$

Abstract

We consider the easy-plane limit of bipartite SU($N$) Heisenberg Hamiltonians which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary $N$, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$-colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $N\le 5$ and valence-bond order for $N>5$. By introducing SU($N$) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $N\le 5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$, suggesting that easy-plane deconfined criticality runs away generically to a first order transition for small-$N$.

8 pages, 8 figures, 1 table

References in corpus (14)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• First-order phase transition in easy-plane quantum antiferromagnets
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Superfluid Insulator Transitions of Hard-Core Bosons on the Checkerboard Lattice
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Nature of the antiferromagnetic to valence-bond-solid quantum phase transition in a 2D XY-model with four-site interactions

Cited by in corpus (19)

• Deconfined quantum critical points: symmetries and dualities
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Deconfined Quantum Critical Point on the Triangular Lattice
• Majorana Loop Models for Measurement-Only Quantum Circuits
• New easy-plane ${\mathbb{CP}}^{N-1}$ fixed points
• Slater and Mott insulating states in the SU(6) Hubbard model
• First order phase transitions in the square lattice "easy-plane" J-Q model
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Bandwidth controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor
• Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Quantum criticality and confinement in weak Mott insulators
• $XY$-VBS phase boundary for the square-lattice $J_1$-$J_2$ $XXZ$ model with the ring exchange