Integrable Matrix Product States from boundary integrability

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the "square root relation", because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the "symmetric pairs" $(SU(N),SO(N))$ and $(SO(N),SO(D)\otimes SO(N-D))$, where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor modifications, v4: minor modification

Exact dynamics in dual-unitary quantum circuits

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs

Integrability of 1D1D Lindbladians from operator-space fragmentation

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: $(i)$ the space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; $(ii)$ the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimension.Comment: 8 pages, no figures; v2: minor revisio

Quantum quenches to the attractive one-dimensional Bose gas: exact results

We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function g2. Copyright L. Piroli et al

Correlations and diagonal entropy after quantum quenches in XXZ chains

We study quantum quenches in the XXZ spin-1/2 Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasi-local conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we compute the diagonal entropy in the post-quench steady state. By careful finite-size scaling analyses of the exact diagonalization results, we show that the diagonal entropy is equal to one half the Yang-Yang entropy corresponding to the complete GGE. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE

Thermodynamic symmetry resolved entanglement entropies in integrable systems

We develop a general approach to compute the symmetry-resolved Rényi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the Gärtner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal states, finding good agreement. As an application, we provide analytic predictions for the asymptotic value of the SREE following a quantum quench

Economic impact of remote monitoring on ordinary follow-up of implantable cardioverter defibrillators as compared with conventional in-hospital visits: a single-center prospective and randomized study

Few data are available on actual follow-up costs of remote monitoring (RM) of implantable defibrillators (ICD). Our study aimed at assessing current direct costs of 1-year ICD follow-up based on RM compared with conventional quarterly in-hospital follow-ups. Methods and results Patients (N=233) with indications for ICD were consecutively recruited and randomized at implant to be followed up for 1 year with standard quarterly inhospital visits or by RM with one in-hospital visit at 12 months, unless additional in-hospital visits were required due to specific patient conditions or RM alarms. Costs were calculated distinguishing between provider and patient costs, excluding RM device and service cost. The frequency of scheduled in-hospital visits was lower in the RM group than in the control arm. Follow-up required 47 min per patient/year in the RM arm versus 86 min in the control arm (p=0.03) for involved physicians, generating cost estimates for the provider of USD 45 and USD 83 per patient/- year, respectively. Costs for nurses were comparable. Overall, the costs associated with RM and standard follow-up were USD 103±27 and 154±21 per patient/year, respectively (p=0.01). RM was cost-saving for the patients: USD 97±121 per patient/year in the RM group versus 287± 160 per patient/year (p=0.0001). Conclusion The time spent by the hospital staff was significantly reduced in the RM group. If the costs for the device and service are not charged to patients or the provider, patients could save about USD 190 per patient/year while the hospital could save USD 51 per patient/year