Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.Comment: 46 pages, 13 figures. To appear in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body Systems"; v2 minor revision. As appears in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body Systems

From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the N\ue9el and tilted N\ue9el states. We apply the Quantum Transfer Matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM's. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t0, after which the integral equations have to be modified. In some regimes, t0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the N\ue9el state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the N\ue9el, tilted N\ue9el and tilted ferromagnet states

Quasi-local conserved charges and spin transport in spin-1 integrable chains

We consider the integrable one-dimensional spin-1 chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-1/2 model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-1 Babujian-Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-1 ZF chain. Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded. Using the Mazur inequality, we show that, as for the XXZ model, these quasi-local charges are enough to prove that the high-temperature spin Drude weight is non-vanishing in the thermodynamic limit, thus establishing ballistic spin transport at high temperature

Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations

Entanglement evolution and generalised hydrodynamics: noninteracting systems

The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled

What is an integrable quench?

Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local conserved charges that are odd under space reflection. We show that this class includes the states which can be related to integrable boundary conditions in an appropriate rotated channel, in loose analogy with the picture in quantum field theory. Furthermore, we provide an efficient method to test integrability of given initial states. We revisit the recent literature of global quenches in several models and show that, in all of the cases where closed-form analytical results could be obtained, the initial state is integrable according to our definition. In the prototypical example of the XXZ spin-s chains we show that integrable states include two-site product states but also larger families of matrix product states with arbitrary bond dimension. We argue that our results could be practically useful for the study of quantum quenches in generic integrable models

Avaliação clínica da mortalidade precoce após fratura de quadril no idoso: estudo prospectivo / Clinical evaluation of early mortality following hip fracture in the elderly: a prospective study

Para avaliar a mortalidade precoce de idosos que apresentaram fraturas do quadril tratadas cirurgicamente neste hospital, no período de 11 de dezembro de 2020 a 30 de abril de 2021, foram realizados interrogatórios em busca de fatores que poderiam estar relacionados a esse desfecho, como sexo, idade, tipo de fratura, cirurgia realizada, comorbidades, tempo de internação até a cirurgia, tempo de internação total e complicações, incluindo óbito. Com uma amostra final de 74 (setenta e quatro) pacientes, 16 (dezesseis), 21,5%, evoluíram com morte nos primeiros 90 (noventa) dias. Este estudo demonstrou que elevados risco cirúrgico, tempo de internação hospitalar e tempo entre a data do trauma e o procedimento cirúrgico contribuíram para o aumento da morbimortalidade nesses pacientes. Além disso, a maioria desses pacientes eram mulheres e receberam transfusão sanguínea. Assim, é importante reduzir o tempo total de hospitalização e evitar transfusão sanguínea em pacientes sem sintomas de anemia ou com níveis de Hb ≥ de 8 g/dl.

Low-temperature transport in out-of-equilibrium XXZ chains

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio \u3b6=x/t. By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures but described by non-trivial functions of \u3b6. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width \u394\u3b6 1dT emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of \u3b6 for all local observables

Via posterior versus via anterior para artroplastia total do quadril: revisão sistemática e metanálise de estudos clínicos randomizados

Objective: to compare the clinical and surgical outcomes of the posterior approach versus the anterior approach for primary total hip arthroplasty. Methods: a systematic review of randomized controlled trials was conducted following the standard guidelines recommended by Cochrane Handbook for Systematic Reviews of Interventions and Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Two independent reviewers searched for randomized controlled trials comparing the posterior approach with the anterior approach for THA. The search was performed on three different databases: PubMed, Cochrane and Virtual Health Library. Results: The systematic review included ten studies with a total of 774 patients. The posterior approach showed a shorter operative time, which was on average mean of 15.98 minutes faster, (95% CI 11.21 to 20.76, p <0.00001). The anterior approach showed a shorter length of hospital stay, on average 0.31 day or about eight hours shorter (95% CI 0.12 to 0.51, p=0.002) and greater earlier improvement in functional outcomes up to six months (mean Harris Hip Score of 4 points greater, 95% CI 2.23 to 5.88, p < 0.0001). Conclusion: The posterior approach showed a shorter operative time, while the anterior approach has the potential to decrease the length of hospitalization and provide greater short-term functional restoration.Objetivo: Comparar os resultados clínicos e cirúrgicos da artroplastia total do quadril primária realizada pela via posterior versus a via anterior. Métodos: Foi realizada uma revisão sistemática de acordo com as diretrizes recomendadas pela Cochrane Handbook for Systematic Reviews of Interventions e Preferred Reporting Items for Systematic Reviews and Meta-Analyses. Dois pesquisadores independentes buscaram ensaios clínicos randomizados que compararam a via posterior com a via anterior para ATQ. A busca foi realizada em três diferentes bases de dados: PubMed, Cochrane e Biblioteca Virtual em Saúde. Resultados: A revisão sistemática incluiu dez estudos totalizando 774 pacientes. A via posterior apresentou um tempo operatório mais curto, que foi, em média, 15.98 minutos mais rápido do que a via anterior (IC 95% 11.21 a 20.76, p<0.00001). A via anterior apresentou menor tempo de internação, em média 0.31 dia ou cerca de oito horas mais curto (IC 95% 0.12 a 0.51, p=0.002) e melhores resultados funcionais em até seis meses de seguimento, em média 4 pontos a mais pelo Harris Hip Score (IC 95%, 2.23 a 5.88, p< 0.0001). Conclusões: A via posterior apresentou menor tempo operatório, enquanto que a via anterior demonstrou o potencial de reduzir o tempo de hospitalização e oferecer melhores resultados clínicos no curto prazo.Dados abertos - Sucupira - Teses e dissertações (2020