Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori ...
The journal of high energy physics,
05/2017, Letnik:
2017, Številka:
5
Journal Article
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A
bstract
We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. ...Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |
Z
(
β
+
it
)|
2
as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.
A
bstract
We compute the entanglement and Rényi entropy growth after a global quench in various dimensions in free scalar field theory. We study two types of quenches: a boundary state quench and a ...global mass quench. Both of these quenches are investigated for a strip geometry in 1, 2, and 3 spatial dimensions, and for a spherical geometry in 2 and 3 spatial dimensions. We compare the numerical results for massless free scalars in these geometries with the predictions of the analytical quasiparticle model based on EPR pairs, and find excellent agreement in the limit of large region sizes. At subleading order in the region size, we observe an anomalous logarithmic growth of entanglement coming from the zero mode of the scalar.
Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly ...distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits
and black holes
, and have been used for benchmarking quantum devices
in tests of quantum advantage
. However, creating random ensembles has necessitated a high degree of spatio-temporal control
placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization
. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 10
experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics
and enables applications of this concept in a much wider context
.
Locality from the Spectrum Cotler, Jordan S.; Penington, Geoffrey R.; Ranard, Daniel H.
Communications in mathematical physics,
06/2019, Letnik:
368, Številka:
3
Journal Article
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Essential to the description of a quantum system are its local degrees of freedom, which enable the interpretation of subsystems and dynamics in the Hilbert space. While a choice of local tensor ...factorization of the Hilbert space is often implicit in the writing of a Hamiltonian or Lagrangian, the identification of local tensor factors is not intrinsic to the Hilbert space itself. Instead, the only basis-invariant data of a Hamiltonian is its spectrum, which does not manifestly determine the local structure. This ambiguity is highlighted by the existence of dualities, in which the same energy spectrum may describe two systems with very different local degrees of freedom. We argue that in fact, the energy spectrum alone almost always encodes a unique description of local degrees of freedom when such a description exists, allowing one to explicitly identify local subsystems and how they interact. As a consequence, we can almost always write a Hamiltonian in its local presentation given only its spectrum. In special cases, multiple dual local descriptions can be extracted from a given spectrum, but generically the local description is unique.
We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which ...enables us to systematically construct unitaries that map between wave functionals which are Gaussian with arbitrary perturbative corrections. As an application, we construct a local continuous multiscale entanglement renormalization ansatz (cMERA) circuit that maps an unentangled scale-invariant state to the ground state of φ4 theory to one loop. Our local cMERA circuit corresponds exactly to one-loop Wilsonian renormalization group (RG) flow on the spatial momentum modes. In other words, we establish that perturbative Wilsonian RG on spatial momentum modes can be equivalently recast as a local cMERA circuit in φ4 theory and argue that this correspondence holds more generally. Our analysis also suggests useful numerical ansätze for cMERA in the nonperturbative regime.
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum ...systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single nonrandom quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state k-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that k-designs emerge naturally from generic states in a Hilbert space as well as physical states associated with strongly interacting Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.
Erratum to: Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori ...
The journal of high energy physics,
09/2018, Letnik:
2018, Številka:
9
Journal Article
Recenzirano
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We have found a minor normalization error in some of the plots in this paper. This error has no effect on the qualitative or quantitative conclusions of the paper.
Out-of-time-order (OTO) operators have recently become popular diagnostics of quantum chaos in many-body systems. The usual way they are introduced is via a quantization of classical Lyapunov growth, ...which measures the divergence of classical trajectories in phase space due to the butterfly effect. However, it is not obvious how exactly they capture the sensitivity of a quantum system to its initial conditions beyond the classical limit. In this paper, we analyze sensitivity to initial conditions in the quantum regime by recasting OTO operators for many-body systems using various formulations of quantum mechanics. Notably, we utilize the Wigner phase space formulation to derive an ħ-expansion of the OTO operator for spatial degrees of freedom, and a large spin 1∕s-expansion for spin degrees of freedom. We find in each case that the leading term is the Lyapunov growth for the classical limit of the system and argue that quantum corrections become dominant at around the scrambling time, which is also when we expect the OTO operator to saturate. We also express the OTO operator in terms of propagators and see from a different point of view how it is a quantum generalization of the divergence of classical trajectories.
We develop a variational approximation to the entanglement entropy for scalar ϕ4 theory in 1+1, 2+1, and 3+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We ...find that in 1+1 and 2+1 dimensions, the entanglement entropy of ϕ4 theory as a function of coupling is monotonically decreasing and convex. While ϕ4 theory with positive bare coupling in 3+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ϕ4 with infinitesimal negative bare coupling, an asymptotically free theory known as precariousϕ4 theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ϕ4 theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.
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