Statistical Mechanics
Quantum contact process (1902.04515v1)
Federico Carollo, Edward Gillman, Hendrik Weimer, Igor Lesanovsky
2019-02-12
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting much less is known. So far mainly semi-classical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also from a numerical point of view, from which the system may look fairly simple --- especially in one dimension --- results are lacking. In particular the presence of the absorbing state poses a substantial challenge which appears to affect the reliability of algorithms targeting directly the steady-state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum non-equilibrium systems.
On the continuum limit of the entanglement Hamiltonian (1902.04474v1)
Viktor Eisler, Erik Tonni, Ingo Peschel
2019-02-12
We consider the entanglement Hamiltonian for an interval in a chain of free fermions in its ground state and show that the lattice expression goes over into the conformal one if one includes the hopping to distant neighbours in the continuum limit. For an infinite chain, this can be done analytically for arbitrary fillings and is shown to be the consequence of the particular structure of the entanglement Hamiltonian, while for finite rings or temperatures the result is based on numerical calculations.
Transition temperature scaling in weakly coupled two-dimensional Ising models (1902.04464v1)
Jordan C. Moodie, Manjinder Kainth, Matthew R. Robson, M. W. Long
2019-02-12
We investigate the proposal that for weakly coupled two-dimensional magnets the transition temperature scales with a critical exponent which is equivalent to that of the susceptibility in the underlying two-dimensional model,
. Employing the exact diagonalization of transfer matrices we can determine the critical temperature for Ising models accurately and then fit to approximate this critical exponent. We find an additional logarithm is required to predict the transition temperature, stemming from the fact that the heat capacity exponent
tends to zero for this Ising model, complicating the elementary prediction. We believe that the excitations of the transfer matrix correspond to thermalized topological excitations of the model and find that even the simplest model exhibits significant changes of behavior for the most relevant of these excitations as the temperature is varied.
Local versus global stretched mechanical response in a supercooled liquid near the glass transition (1812.04527v2)
Baoshuang Shang, Jörg Rottler, Pengfei Guan, Jean-Louis Barrat
2018-12-11
Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.
Dynamical Quantum Phase Transition and Quasi Particle Excitation (1902.04421v1)
R. Jafari
2019-02-12
Dynamical phase transitions (DPTs) are signaled by the non-analytical time evolution of the dynamical free energy after quenching some global parameters in quantum systems. The dynamical free energy is calculated from the overlap between the initial and the time evolved states (Loschmidt amplitude). In a recent study it was suggested that DPTs are related to the equilibrium phase transitions (EPTs) (M. Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)). We here study an exactly solvable model, the extended
model, the Loschmidt amplitude of which provides a counterexample. We show analytically that the connection between the DPTs and the EPTs does not hold generally. Analysing also the general compass model as a second example, assists us to propound the physical condition under which the DPT occurs without crossing the equilibrium critical point, and also no DPT by crossing the equilibrium critical point.
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