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Register a new userOn the possibility of complete revivals after quantum quenches to a critical point
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In a recent letter, J. Cardy, Phys. Rev. Lett. textbf{112}, 220401 (2014), the author made a very interesting observation that complete revivals of quantum states after quantum quench can happen in a period which is a fraction of the system size. This is possible for critical systems that can be described by minimal conformal field theories (CFT) with central charge $c<1$. In this article, we show that these complete revivals are impossible in microscopic realizations of those minimal models. We will prove the absence of the mentioned complete revivals for the critical transverse field Ising chain analytically, and present numerical results for the critical line of the XY chain. In particular, for the considered initial states, we will show that criticality has no significant effect in partial revivals. We also comment on the applicability of quasi-particle picture to determine the period of the partial revivals qualitatively. In particular, we detect a regime in the phase diagram of the XY chain which one can not determine the period of the partial revivals using the quasi-particle picture.
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We describe several results concerning global quantum quenches from states with short-range correlations to quantum critical points whose low-energy properties are described by a 1+1-dimensional conformal field theory (CFT), extending the work of Calabrese and Cardy (2006): (a) for the special class of initial states discussed in that paper we show that, once a finite region falls inside the horizon, its reduced density matrix is exponentially close in $L_2$ norm to that of a thermal Gibbs state; (b) small deformations of this initial state in general lead to a (non-Abelian) generalized Gibbs distribution (GGE) with, however, the possibility of parafermionic conserved charges; (c) small deformations of the CFT, corresponding to curvature of the dispersion relation and (non-integrable) left-right scattering, lead to a dependence of the speed of propagation on the initial state, as well as diffusive broadening of the horizon.
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results are used to confirm the validity of a previously proposed analytical Ansatz for the initial state in the sinh-Gordon quench.
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $betall L$. For times $t$ such that $ell/2<t<(L-ell)/2$ the reduced density matrix of a subsystem of length $ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/beta$. However, for minimal models with $c<1$ (more generally, rational CFTs), at times which are integer multiples of $L/2$ (for periodic boundary conditions, $L$ for open boundary conditions) there are (in general, partial) revivals at which $cal F$ is $O(1)$, leading to an eventual complete revival with ${cal F}=1$. There is also interesting structure at all rational values of $t/L$, related to properties of the CFT under modular transformations. At early times $t!ll!(Lbeta)^{1/2}$ there is a universal decay ${cal F}simexpbig(!-!(pi c/3)Lt^2/beta(beta^2+4t^2)big)$. The effect of an irrelevant non-integrable perturbation of the CFT is to progressively broaden each revival at $t=nL/2$ by an amount $O(n^{1/2})$.
In multi-band metals quasi-particles arising from different atomic orbitals coexist at a common Fermi surface. Superconductivity in these materials may appear due to interactions within a band (intra-band) or among the distinct metallic bands (inter-band). Here we consider the suppression of superconductivity in the intra-band case due to hybridization. The fluctuations at the superconducting quantum critical point (SQCP) are obtained calculating the response of the system to a fictitious space and time dependent field, which couples to the superconducting order parameter. The appearance of superconductivity is related to the divergence of a generalized susceptibility. For a single band superconductor this coincides with the textit{Thouless criterion}. For fixed chemical potential and large hybridization, the superconducting state has many features in common with breached pair superconductivity with unpaired electrons at the Fermi surface. The T=0 phase transition from the superconductor to the normal state is in the universality class of the density-driven Bose-Einstein condensation. For fixed number of particles and in the strong coupling limit, the system still has an instability to the normal sate with increasing hybridization.
We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.
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