Entanglement and its relation to energy variance for local one-dimensional Hamiltonians
We explore the relation between the entanglement of a pure state and its energy variance for a local one-dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance $δ^2$ for $$\textit{N}$$ spins, with bond dimension scaling as $$\sqrt{N}D^{1/δ}_0$$, where $$D_0$$ > 1 is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the construction on two different models and compare the local reduced density matrices of the resulting states to the corresponding thermal equilibrium. Our results suggest that the spatially homogeneous states with logarithmically decreasing variance, which can be constructed efficiently, do converge to the thermal equilibrium in the thermodynamic limit, while the same is not true if the variance remains constant.
- Research Organization:
- Princeton Univ., NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); German Research Foundation (DFG); European Research Council (ERC); National Science Foundation (NSF)
- Grant/Contract Number:
- SC0016244; 742102; NSF PHY-1748958
- OSTI ID:
- 1616366
- Alternate ID(s):
- OSTI ID: 1802887
- Journal Information:
- Physical Review B, Journal Name: Physical Review B Vol. 101 Journal Issue: 14; ISSN 2469-9950
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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