Does a Single Eigenstate Encode the Full Hamiltonian?

Garrison, James R.; Grover, Tarun

doi:10.1103/physrevx.8.021026

Cited by 257 publications

(314 citation statements)

References 82 publications

(67 reference statements)

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“…It is conjectured and supported by numerical evidence in [7] that (2) holds true for all operators only as long as V A /V 1; here V A is the volume of subsystem A and V is the total volume. 1 Hence, subsystem ETH holds true only in this limit.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 89%

“…If the subsystem ETH is true, the entanglement entropies of the reduced density matrices should also be the same. A large number of verifications of the hypothesis, involving the numerical extraction of eigenstates by exact diagonalization, has been carried out in various lattice models [3,[6][7][8][9]. It has also been proved for quantum systems having a classical chaotic limit [2,10].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 97%

“…It has been recently shown in [7] that if ETH holds good, then it allows one to use a single eigenstate to extract properties of the Hamiltonian at arbitrary temperatures.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…More precisely, [7] also conjectures that for V A /V > 0 the set of operators spanned by H n A for n > 1 do not satisfy the ETH relation (2). Here H A is the Hamiltonian restricted to the subsystem A.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…For the one norm, numerics in [7] for the 1 + 1 dimensional quantum spin 1/2 model with both longitudinal and transverse field turned on, suggest that there is a scaling of this distance with the subsystem fraction. In the regime the subsystem size ( ) is much smaller than the system size (L) and β smaller than all scales, then the trace norm distance tends to zero at least linearly with 1/L.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

See 4 more Smart Citations

Thermality of eigenstates in conformal field theories

et al. 2017

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The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-d conformal field theories, consisting of quasi-primaries of the identity module, which satisfy the hypothesis only at the leading order in large central charge. In the context of subsystem ETH, this plays a role in the deviation of the reduced density matrices, corresponding to a finite energy density eigenstate from its hypothesized thermal approximation. The universal deviation in terms of the square of the trace-square distance goes as the 8th power of the subsystem fraction and is suppressed by powers of inverse central charge (c). Furthermore, the non-universal deviations from subsystem ETH are found to be proportional to the heavy-light-heavy structure constants which are typically exponentially suppressed in h/c, where h is the conformal scaling dimension of the finite energy density state. We also examine the effects of the leading finite size corrections.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 89%

Section: Introduction and Summary Of Resultsmentioning

confidence: 97%

“…It has been recently shown in [7] that if ETH holds good, then it allows one to use a single eigenstate to extract properties of the Hamiltonian at arbitrary temperatures.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

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Thermality of eigenstates in conformal field theories

et al. 2017

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Extensibility of Hohenberg–Kohn Theorem to General Quantum Systems

Mao

Gao

et al. 2022

Adv Quantum Tech

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The Hohenberg-Kohn (HK) theorem for interacting electrons is a cornerstone of modern electronic structure calculations. For a general quantum system, a HK-type Hamiltonian in the form of Ĥhk {g i } = Ĥint + ∑ i g i Ôi can always be defined, by grouping those terms with fixed or preknown coefficients into an internal part of the Hamiltonian Ĥint , and factorizing the remaining as the superposition of a set of Hermitian operators { Ôi }. It is asked whether the HK theorem can be extended to such a general setting, so that the ground-state expectation values of { Ôi } as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. It is shown that the question can be addressed by the invertibility of generalized density correlation matrix (GDCM) defined with respect to the { Ôi } operators. This criterion is applied to several representative examples, including the quantum Ising dimer, frustration-free systems, N-level quantum systems and a fermionic Hubbard chain. It is suggested that for a finite-size system, finding an invertible GDCM under one single {g i } configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space.

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