Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians

Abstract

We consider bipartite SU($N$) spin Hamiltonians with a fundamental representation on one sublattice and a conjugate to fundamental on the other sublattice. By mapping these antiferromagnets to certain classical loop models in one higher dimension, we provide a practical strategy to write down a large family of SU($N$) symmetric spin Hamiltonians that satisfy Marshall's sign condition. This family includes all previously known sign-free SU($N$) spin models in this representation and in addition provides a large set of new models that are Marshall positive and can hence be studied efficiently with quantum Monte Carlo methods. As an application of our idea to the square lattice, we show that in addition to Sandvik's $Q$-term, there is an independent non-trivial four-spin $R$-term that is sign-free. Using numerical simulations, we show how the $R$-term provides a new route to the study of quantum criticality of Néel order.

References in corpus (23)

• The density-matrix renormalization group
• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Fate of CP(N-1) fixed points with q-monopoles
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Impurity spin texture at a deconfined quantum critical point
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Ground States of the SU(N) Heisenberg Model
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Simulations of pure and doped low-dimensional spin-1/2 gapped systems
• Example of a first-order Néel to Valence-Bond-Solid transition in two-dimensions
• Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets

Cited by in corpus (15)

• Quantum Critical Points and the Sign Problem
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• A perspective on machine learning and data science for strongly correlated electron problems
• First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$
• Deconvolving the components of the sign problem
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets
• On the Fermion Sign Problem in Imaginary-Time Projection Continuum Quantum Monte Carlo with Local Interaction
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet