Energy density of variational states

Abstract

We show, in several important and general cases, that a low variational energy density of a trial state is possible even when the trial state represents a different phase from the ground state. Specifically, we ask whether the ground state energy density of a Hamiltonian whose ground state is in phase A can be approximated to arbitrary accuracy by a wavefunction which represents a different phase B. We show this is indeed the case when A has discrete symmetry breaking order in one dimension or topological order in two dimensions, while B is disordered. We argue that, if reasonable conditions of physicality are imposed upon the trial wavefunction, then this is not possible when A has discrete symmetry breaking in dimensions greater than one and B is symmetric, or when A is topologically trivial and B has topological order.

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Cited by in corpus (11)

• Quantum Spin Liquids
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• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Bridging Perturbative Expansions with Tensor Networks
• On the stability of topological order in tensor network states
• On tensor network representations of the (3+1)d toric code
• Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
• Partons from stabilizer codes
• Z${}_2$ topological orders in kagomé dipolar systems: Feedback from Rydberg quantum simulator