Abstract We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult (2 + 1) d quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code $${{\mathbb{Z}}}_{2}$$ Z 2 topological ordered state and the Kagome $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars, and minimal computational costs. Our method, therefore, establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.
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A model of persistent breaking of continuous symmetry
We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of thelong-range vector models, with O(m) and O(N-m) global symmetry groups,perturbed by double-trace operators.Using conformal perturbation theorywe find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneousbreaking of global symmetry. Namely, at finite temperature the lower rank group is broken,with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.
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- Award ID(s):
- 2013812
- NSF-PAR ID:
- 10348657
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 12
- Issue:
- 6
- ISSN:
- 2542-4653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.12.6.181
