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Register a new userAnomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems
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We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k to 0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.
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We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seems to support the existence of rare states, i.e. states where the observables take expectation values which are different compared to the typical ones sampled by the micro-canonical distribution. In the case of sparse random matrices we also extract the finite size behavior of two different time scales associated with the thermalization process.
The dimensionality of the electronic and magnetic structure of a given material is generally predetermined by its crystal structure. Here, using elastic and inelastic neutron scattering combined with magnetization measurements, we find unusual magnetic behavior in three-dimensional (3D) Ba2CoO4. In spite of isolated CoO4 tetrahedra, the system exhibits a 3D noncollinear antiferromagnetic order in the ground state with an anomalously large Curie-Weiss temperature of 110 K compared to TN = 26 K. More unexpectedly, spin dynamics displays quasi-2D spin wave dispersion with an unusually large spin gap, and 1D magnetoelastic coupling. Our results indicate that Ba2CoO4 is a unique system for exploring the interplay between isolated polyhedra, low-dimensional magnetism, and novel spin states in oxides.
The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. The GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle, and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables.
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a `quantum quench in which a parameter in the hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.
We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behaviour that is compatible with eventual thermalization.
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