Related papers: Efficient variational diagonalization of fully man…
We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters…
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of…
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The…
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
The inverse problem of 'eigenstates-to-Hamiltonian' is considered for an open chain of $N$ quantum spins in the context of Many-Body-Localization. We first construct the simplest basis of the Hilbert space made of $2^N$ orthonormal…
We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which…
Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and…