اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExtensive entropy from unitary evolution
84
0
0.0
(
0
)
تأليف
Yichen Huang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].
قيم البحث
اقرأ أيضاً
The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entang
lement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.
We investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. We compare two different limits of the measurement problem, the stochastic quantum-state diffusion protocol corresponding to infinite
small jumps per unit of time and the no-click limit, corresponding to post-selection and described by a non-Hermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the measurement strength $gamma$ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noise-induced disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The non-Hermitian Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging here for a model which lacks any continuous symmetry, and the entanglement transition into the area law.
Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed self-organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable evolving
through an extremal dynamics process, as in the Bak-Sneppen model representing a prototype of Self-Organized Criticality. The network topology is in turn shaped by the fitness variable itself, as in the fitness network model. The system self-organizes to a nontrivial state, characterized by a power-law decay of dynamical and topological quantities above a critical threshold. The interplay between topology and dynamics in the system is the key ingredient leading to an unexpected behaviour of these quantities.
The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, inclu
ding strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the non-linear elastic exponent, the yielding strain/stress and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path towards understanding complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.
We introduce an approach to compute reduced density matrices for local quantum unitary circuits of finite depth and infinite width. Suppose the time-evolved state under the circuit is a matrix-product state with bond dimension $D$; then the reduced d
ensity matrix of a half-infinite system has the same spectrum as an appropriate $Dtimes D$ matrix acting on an ancilla space. We show that reduced density matrices at different spatial cuts are related by quantum channels acting on the ancilla space. This quantum channel approach allows for efficient numerical evaluation of the entanglement spectrum and Renyi entropies and their spatial fluctuations at finite times in an infinite system. We benchmark our numerical method on random unitary circuits, where many analytic results are available, and also show how our approach analytically recovers the behaviour of the kicked Ising model at the self-dual point. We study various properties of the spectra of the reduced density matrices and their spatial fluctuations in both the random and translation-invariant cases.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
