Related papers: Improved Hilbert space exploration algorithms for …
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
The central challenge for describing the dynamics in open quantum systems is that the Hilbert space of typical environments is too large to be treated exactly. In some cases, such as when the environment has a short memory time or only…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
Understanding the physics of strongly correlated materials is one of the grand challenge problems for physics today. A large class of scientifically interesting materials, from high-$T_c$ superconductors to spin liquids, involve medium to…
Here a finite-Lieb-lattice quantum computing circuit consisting of spin-1/2 quantum bits (qubits) and triplet couplers is designed. Important gradient - quantum entanglement - is analysed. This type of design could be realised in a vast…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
Entanglement is the fundamental difference between classical and quantum systems and has become one of the guiding principles in the exploration of high- and low-energy physics. The calculation of entanglement entropies in interacting…
We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
We construct upper bounds on entanglement entropies of many-body quantum states that have fixed energy expectation values with respect to geometrically local Hamiltonians. Our focus is on entanglement entropies of subsystems that make up…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
We review various theoretical methods that have been used in recent years to calculate dynamical correlation functions of many-body systems. Time-dependent correlation functions and their associated frequency spectral densities are the…
We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution,…
Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine…
We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…
We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of…