Energy-filtered quantum states and the emergence of non-local correlations
arXiv:2405.02158 · doi:10.1103/PhysRevLett.133.240401
Abstract
Energy-filtered quantum states are promising candidates for efficiently simulating thermal states. We explore a protocol designed to transition a product state into an eigenstate located in the middle of the spectrum; this is achieved by gradually reducing its energy variance, which allows us to comprehensively understand the crossover phenomenon and the subsequent convergence towards thermal behavior. We introduce and discuss three energy-filtering regimes (short, medium and long), and we interpret them as stages of thermalization. We show that the properties of the filtered states are locally indistinguishable from those of time-averaged density matrices, routinely employed in the theory of thermalization. On the other hand, unexpected non-local quantum correlations are generated in the medium regimes and are witnessed by the Rényi entanglement entropies of subsystems, which we compute via replica methods. Specifically, two-point correlation functions break cluster decomposition and the entanglement entropy of large regions scales as the logarithm of the volume during the medium filter time.
14 pages, 7 figures
References in corpus (22)
- The density-matrix renormalization group in the age of matrix product states
- Real time evolution using the density matrix renormalization group
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Strong and weak thermalization of infinite non-integrable quantum systems
- Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
- Algorithms for quantum simulation at finite energies
- Twist operators in higher dimensions
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Extensive multipartite entanglement from su(2) quantum many-body scars
- Temporal Entanglement in Chaotic Quantum Circuits
- Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
- Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
- Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
- Asymptotic Quantum Many-Body Scars
- Microcanonical windows on quantum operators
- Approximating the long time average of the density operator: Diagonal ensemble
- Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
- Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers
- Efficient Quantum Algorithm for Filtering Product States
- Matrix product state approximations to quantum states of low energy variance
- On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system
- Probing Off-diagonal Eigenstate Thermalization with Tensor Networks