Strong and weak thermalization of infinite non-integrable quantum systems

When a non-integrable system evolves out of equilibrium for a long time, local observables are expected to attain stationary expectation values, independent of the details of the initial state. However, intriguing experimental results with ultracold gases have shown no thermalization in non-integrable settings, triggering an intense theoretical effort to decide the question. Here we show that the phenomenology of thermalization in a quantum system is much richer than its classical counterpart. Using a new numerical technique, we identify two distinct thermalization regimes, strong and weak, occurring for different initial states. Strong thermalization, intrinsically quantum, happens when instantaneous local expectation values converge to the thermal ones. Weak thermalization, well-known in classical systems, happens when local expectation values converge to the thermal ones only after time averaging. Remarkably, we find a third group of states showing no thermalization, neither strong nor weak, to the time scales one can reliably simulate.Comment: 12 pages, 21 figures, including additional materia

Multiscaling at Point J: Jamming is a Critical Phenomenon

We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for ``Point J'' of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T = 0 jamming transition as a function of packing density is a {\it second order} phase transition. Additionally we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.Comment: 4 pages, 5 figures; extensive new numerical data; final version in press at PR

Bose Glass in Large N Commensurate Dirty Boson Model

The large N commensurate dirty boson model, in both the weakly and strongly commensurate cases, is considered via a perturbative renormalization group treatment. In the weakly commensurate case, there exists a fixed line under RG flow, with varying amounts of disorder along the line. Including 1/N corrections causes the system to flow to strong disorder, indicating that the model does not have a phase transition perturbatively connected to the Mott Insulator-Superfluid (MI-SF) transition. I discuss the qualitative effects of instantons on the low energy density of excitations. In the strongly commensurate case, a fixed point found previously is considered and results are obtained for higher moments of the correlation functions. To lowest order, correlation functions have a log-normal distribution. Finally, I prove two interesting theorems for large N vector models with disorder, relevant to the problem of replica symmetry breaking and frustration in such systems.Comment: 16 pages, 7 figure

An area law for entanglement from exponential decay of correlations

Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics suggests that an area law should hold whenever there is exponential decay of correlations in the system, a property found, for instance, in non-critical phases of matter. However, the existence of quantum data-hiding state--that is, states having very small correlations, yet a volume scaling of entanglement--was believed to be a serious obstruction to such an implication. Here we prove that notwithstanding the phenomenon of data hiding, one-dimensional quantum many-body states satisfying exponential decay of correlations always fulfil an area law. To obtain this result we combine several recent advances in quantum information theory, thus showing the usefulness of the field for addressing problems in other areas of physics.Comment: 8 pages, 3 figures. Short version of arXiv:1206.2947 Nature Physics (2013

Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice

There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-1/2 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux-smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED$_3$) with an emergent $\mathrm{SU}(8)$ flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.Comment: 14 pages, 8 figure

Evolution of the far-infrared luminosity functions in the Spitzer Wide-area Infrared Extragalactic Legacy Survey

We present new observational determination of the evolution of the rest-frame 70 and 160 micron and total infrared (TIR) galaxy luminosity functions (LFs) using 70 micron data from the Spitzer Wide-area Infrared Extragalactic Legacy Survey (SWIRE). The LFs were constructed for sources with spectroscopic redshifts only in the XMM-LSS and Lockman Hole fields from the SWIRE photometric redshift catalogue. The 70 micron and TIR LFs were constructed in the redshift range 0<z<1.2 and the 160 micron LF was constructed in the redshift range 0<z<0.5 using a parametric Bayesian and the vmax methods. We assume in our models, that the faint-end power-law index of the LF does not evolve with redshifts. We find the the double power-law model is a better representation of the IR LF than the more commonly used power-law and Gaussian model. We model the evolution of the FIR LFs as a function of redshift where where the characteristic luminosity, $L^\ast$ evolve as \propto(1+z)^{\alpha_\textsc{l}}. The rest-frame 70 micron LF shows a strong luminosity evolution out to z=1.2 with alpha_l=3.41^{+0.18}_{-0.25}. The rest-frame 160 micron LF also showed rapid luminosity evolution with alpha_l=5.53^{+0.28}_{-0.23} out to z=0.5. The rate of evolution in luminosity is consistent with values estimated from previous studies using data from IRAS, ISO and Spitzer. The TIR LF evolves in luminosity with alpha_l=3.82^{+0.28}_{-0.16} which is in agreement with previous results from Spitzer 24 micron which find strong luminosity evolution. By integrating the LF we calculated the co-moving IR luminosity density out to z=1.2, which confirm the rapid evolution in number density of LIRGs and ULIRGs which contribute ~68^{+10}_{-07} % to the co-moving star formation rate density at z=1.2. Our results based on 70 micron data confirms that the bulk of the star formation at z=1 takes place in dust obscured objects.Comment: 17 pages, 14 figure

Random Unitaries Give Quantum Expanders

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur