Quantum Critical Point and Entanglement in a Matrix Product Ground State

In this paper, we study the entanglement properties of a spin-1 model the exact ground state of which is given by a Matrix Product state. The model exhibits a critical point transition at a parameter value a=0. The longitudinal and transverse correlation lengths are known to diverge as a tends to zero. We use three different entanglement measures S(i) (the one-site von Neumann entropy), S(i,j) (the two-body entanglement) and G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter a is varied. The entanglement length, associated with S(i,j), is found to diverge in the vicinity of the quantum critical point a=0. The first derivative of the entanglement measure E (=S(i), S(i,j)) w.r.t. the parameter a also diverges. The first derivative of G(2,n) w.r.t. a does not diverge as a tends to zero but attains a maximum value at a=0. At the QCP itself all the three entanglement measures become zero. We further show that multipartite correlations are involved in the QPT at a=0.Comment: 14 pages, 6 figure

The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points

We study the scaling of the decoherence factor of a qubit (spin-1/2) using the central spin model in which the central spin (qubit) is globally coupled to a transverse XY spin chain. The aim here is to study the non-equilibrium generation of decoherence when the spin chain is driven across (along) quantum critical points (lines) and derive the scaling of the decoherence factor in terms of the driving rate and some of the exponents associated with the quantum critical points. Our studies show that the scaling of logarithm of decoherence factor is identical to that of the defect density in the final state of the spin chain following a quench across isolated quantum critical points for both linear and non-linear variations of a parameter even if the defect density may not satisfy the standard Kibble-Zurek scaling. However, one finds an interesting deviation when the spin chain is driven along a critical line. Our analytical predictions are in complete agreement with numerical results. Our study, though limited to integrable two-level systems, points to the existence of a universality in the scaling of the decoherence factor which is not necessarily identical to the scaling of the defect density.Comment: 5 pages, 2 figures, Final and accepted versio

Metabolic syndrome and migraine.

Migraine and metabolic syndrome are highly prevalent and costly conditions. The two conditions coexist, but it is unclear what relationship may exist between the two processes. Metabolic syndrome involves a number of findings, including insulin resistance, systemic hypertension, obesity, a proinflammatory state, and a prothrombotic state. Only one study addresses migraine in metabolic syndrome, finding significant differences in the presentation of metabolic syndrome in migraineurs. However, controversy exists regarding the contribution of each individual risk factor to migraine pathogenesis and prevalence. It is unclear what treatment implications, if any, exist as a result of the concomitant diagnosis of migraine and metabolic syndrome. The cornerstone of migraine and metabolic syndrome treatments is prevention, relying heavily on diet modification, sleep hygiene, medication use, and exercise

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part II: Application to the Many-Body Problem

We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [11]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean field plus spin wave approach. First, we determine shifts in the mean field phase border, which are most pronounced in the low density regime. Second, the investigation of the strong coupling limit reveals the existence of a new collective mode, which emerges as a consequence of enhanced symmetries in this regime. Third, we show that the Ising type phase transition, driven first order via the competition of long wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.Comment: 22 pages, 5 figure

Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model

We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a distance r are connected with a non-random ferromagnetic bond with a probability that falls algebraically with the distance between the sites as 1/r^{d+\sigma}. The interplay of the fluctuations due to dilutions together with the quantum fluctuations due to the transverse field leads to an interesting critical behaviour. The exponents at the critical fixed point (which is an infinite randomness fixed point (IRFP)) are related to the classical "long-range" percolation exponents. The most interesting observation is that the gap exponent \psi is exactly obtained for all values of \sigma and d. Exponents depend on the range parameter \sigma and show a crossover to short-range values when \sigma >= 2 -\eta_{SR} where \eta_{SR} is the anomalous dimension for the conventional percolation problem. Long-range connections are also found to tune the strength of the Griffiths phase.Comment: 5 pages, 1 figure, To appear in Phys. Rev.

Oscillating fidelity susceptibility near a quantum multicritical point

We study scaling behavior of the geometric tensor $\chi_{\alpha,\beta}(\lambda_1,\lambda_2)$ and the fidelity susceptibility $(\chi_{\rm F})$ in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of $\chi_{\rm F}$) is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of $\lambda$ along the generic direction $\lambda_1\sim\lambda_2 = \lambda$ when the system size $L$ is bounded between the shorter and longer correlation lengths characterizing the MCP: $1/|\lambda|^{\nu_1}\ll L\ll 1/|\lambda|^{\nu_2}$, where $\nu_1<\nu_2$ are the two correlation length exponents characterizing the system. We find that the scaling of the maxima of the components of $\chi_{\alpha\beta}$ is associated with emergence of quasi-critical points at $\lambda\sim 1/L^{1/\nu_1}$, related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit $L\gg 1/|\lambda|^{\nu_2}$, which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.Comment: 12 pages, 9 figure

Fidelity susceptibility and general quench near an anisotropic quantum critical point

We study the scaling behavior of fidelity susceptibility density $(\chi_{\rm f})$ at or close to an anisotropic quantum critical point characterized by two different correlation length exponents $\nu_{||}$ and $\nu_{\bot}$ along parallel and perpendicular spatial directions, respectively. Our studies show that the response of the system due to a small change in the Hamiltonian near an anisotropic quantum critical point is different from that seen near an isotropic quantum critical point. In particular, for a finite system with linear dimension $L_{||}$ ($L_{\bot}$) in the parallel (perpendicular) directions, the maximum value of $\chi_{\rm f}$ is found to increases in a power-law fashion with $L_{||}$ for small $L_{||}$, with an exponent depending on both $\nu_{||}$ and $\nu_{\bot}$ and eventually crosses over to a scaling with $L_{\bot}$ for $L_{||}^{1/\nu_{||}} \gtrsim L_{\bot}^{1/\nu_{\bot}}$. We also propose scaling relations of heat density and defect density generated following a quench starting from an anisotropic quantum critical point and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.Comment: 6 pages, 6 pigure

Observability of Quantum Criticality and a Continuous Supersolid in Atomic Gases

We analyze the Bose-Hubbard model with a three-body hardcore constraint by mapping the system to a theory of two coupled bosonic degrees of freedom. We find striking features that could be observable in experiments, including a quantum Ising critical point on the transition from atomic to dimer superfluidity at unit filling, and a continuous supersolid phase for strongly bound dimers.Comment: 4 pages, 2 figures, published version (Editor's suggestion

Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field

We study the quantum dynamics of a one-dimensional spin-1/2 anisotropic XY model in a transverse field when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. The two quenching schemes are called transverse and anisotropic quenching respectively. Our emphasis in this paper is on the anisotropic quenching scheme and we compare the results with those of the other scheme. In the process of anisotropic quenching, the system crosses all the quantum critical lines of the phase diagram where the relaxation time diverges. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrt{\tau}$, where $\tau$ is the characteristic time scale of quenching, a scenario that supports the Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching, there exists an additional non-adiabatic transition, in comparison to the transverse quenching case, with the corresponding probability peaking at an incommensurate value of the wave vector. In the special case in which the system passes through a multi-critical point, the defect density is found to vary as $1/\tau^{1/6}$. The von Neumann entropy of the final state is shown to maximize at a quenching rate around which the ordering of the final state changes from antiferromagnetic to ferromagnetic.Comment: 8 pages, 6 figure

Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field

We study the quenching dynamics of a one-dimensional spin-1/2 $XY$ model in a transverse field when the transverse field $h(=t/\tau)$ is quenched repeatedly between $-\infty$ and $+\infty$. A single passage from $h \to - \infty$ to $h \to +\infty$ or the other way around is referred to as a half-period of quenching. For an even number of half-periods, the transverse field is brought back to the initial value of $-\infty$; in the case of an odd number of half-periods, the dynamics is stopped at $h \to +\infty$. The density of defects produced due to the non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrt{\tau}$ for large $\tau$; however, the magnitude is found to depend on the number of half-periods of quenching. For two successive half-periods, the defect density is found to decrease in comparison to a single half-period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as $1/{\sqrt\tau}$ for large $\tau$ for any number of half-periods, and shows a increase in kink density for small $\tau$ for an even number; the entropy shows qualitatively the same behavior for any number of half-periods. The probability of non-adiabatic transitions and the local entropy saturate to 1/2 and $\ln 2$, respectively, for a large number of repeated quenching.Comment: 5 pages, 3 figure