Related papers: Uniform Matrix Product State in the Thermodynamic …
The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a…
Let $\Psi_n$ be a product of $n$ independent, identically distributed random matrices $M$, with the properties that $\Psi_n$ is bounded in $n$, and that $M$ has a deterministic (constant) invariant vector. Assuming that the probability of…
We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such…
We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable,…
The time-dependent transport through single-molecule magnets coupled to magnetic or non-magnetic electrodes is studied in the framework of the generalized master equation method. We investigate the transient regime induced by the periodic…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain…
By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found.…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
Thermodynamic properties of the quantum Heisenberg spin chains with S = 1/2, 1, and 3/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat,…
Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling…
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurements. We solve a problem raised by the recent work [Liu,…
A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…
We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution…
The pulse-noise approach to systems of classical spins weakly interacting with the bath has been applied to study thermally-activated escape of magnetic nanoparticles over the uniform and nonuniform energy barriers at intermediate and low…
We consider a random process with discrete time formed by singular values of products of truncations of Haar distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives…
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the…
We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states…
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…