Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems

I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped, one-dimensional system. I show that the edge exponent in the probability density function of the work is insensitive to the presence of interactions and can take only one of three values: +1/2, -1/2 and -3/2. It also turns out that there is an interesting interplay between spontaneous symmetry breaking or the presence of bound states and the exponents. For instantaneous global protocols, I find that the presence of the one-particle channel creates dynamical phase transitions in the time evolution.Comment: 5 pages, 2 figures. Revised version published in PR

Entanglement Entropy from the Truncated Conformal Space

A new numerical approach to entanglement entropies of the Renyi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited to study the crossover from massless to massive behavior when the subsystem size is comparable to the correlation length. We apply it to different deformations of massless free fermions, corresponding to the scaling limit of the Ising model in transverse and longitudinal fields. For massive free fermions the exactly known crossover function is reproduced already in very small system sizes. The new method treats ground states and excited states on the same footing, and the applicability for excited states is illustrated by reproducing Renyi entropies of low-lying states in the transverse field Ising model.Comment: 8 pages, 3 figures; v3: some typos corrected, figures replaced; v2: discussion in Sec. 2 expanded, some typos corrected, one new reference adde

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $k\gg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $\lambda$. Moreover for $\lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.Comment: 30 pages, 19 eps figures, LaTeX2e file. Version 2: manuscript accepted for publication; small changes in text and in one of the figure

Sine-Gordon multisoliton form factors in finite volume

Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.Comment: 24 pages, LaTeX2e file, 8 eps figures. v2: notations improved, some explanatory text and references adde

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure

Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics

In this paper we study a (1+1)-dimensional version of the famous Nambu-Jona-Lasinio model of Quantum Chromodynamics (QCD2) both at zero and finite hadron density. We use non-perturbative techniques (non-Abelian bosonization and Truncated Conformal Space Approach). At zero density we describe a formation of fermion three-quark (nucleons and $\Delta$-baryons) and boson (two-quark mesons, six-quark deuterons) bound states and also a formation of a topologically nontrivial phase. At finite hadron density, the model has a rich phase diagram which includes phases with density wave and superfluid quasi-long-range (QLR) order and also a phase of a baryon Tomonaga-Luttinger liquid (strange metal). The QLR order results as a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).Comment: 31 pages, pdflatex file, 7 figures; typos corrected, the version from Phys. Rev.

Supporting Roma Voices

The Supporting Roma Voice project has aimed to address emerging knowledge gaps in the way in which the inclusion of migrant Roma in the UK is being addressed. Specifically, research by Brown, Scullion and Martin (2013) identified a demand from public authorities for social inclusion work directed towards migrant Roma communities to be developed and delivered by members of migrant Roma communities themselves. However, what was also lacking was an adequate evidence base about the settlement of migrant Roma in the UK and the varied experiences associated with this transition. This report explores the views and experiences of a large number of Roma people who have migrated to the UK in recent years. The research was designed in partnership with a team of researchers from the Roma communities and undertaken wholly by these researchers. The research study aimed to explore the following issues: - The settlement and integration experiences of Roma migrants living in areas across the UK. - The specific areas of community relations, housing, education, employment and social welfare and their role in settlement in the UK. - The provision of knowledge that would enable local authorities and other services to enhance the settlement experience of Roma migrants now and in the future. A total of 159 people participated in 19 focus groups, which took place in the following locations: Glasgow, Leicester, London, Oldham, Salford and Sheffield. It should be noted that owing to the heterogeneity of the Roma population this report does not attempt to make definitive statements about the situation and views of all Roma migrants in the UK. This report was co-authored by members of the academic team in partnership with community researchers. The fieldwork was undertaken in early 2016 prior to the UK’s referendum on staying in the European Union

Relative entanglement entropies in 1 + 1-dimensional conformal field theories

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(\u3c11\u2016\u3c10) between two given reduced density matrices \u3c11 and \u3c10 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(\u3c11\u3c1n 1210) and define a set of R\'enyi relative entropies Sn(\u3c11\u2016\u3c10). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i 02\u3d5, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. \ua9 2017, The Author(s)

R\ue9nyi entropies of generic thermodynamic macrostates in integrable systems

We study the behaviour of R\ue9nyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\ue9nyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\ue9nyi entropies after the quench from the dimer and the tilted N\ue9el state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies