相关论文: Optimizing sparse fermionic Hamiltonians

We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem…

We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Mat\'ern class random field. The approximation method is based on the spectral compactness of the…

In this paper we show that inverses of well-conditioned, finite-time Gramians and impulse response matrices of large-scale interconnected systems described by sparse state-space models, can be approximated by sparse matrices. The…

Lattice fermions obeying the Ginsparg-Wilson relation do correctly represent the physical properties related to chirality. This can be achieved by local fermions, which involve an infinite number of couplings, however. For practical…

The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the re-summation of scalars at strong coupling. Then, we…

Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…

We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence…

The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k\ll…

The ground state correlations induced by a general pairing Hamiltonian in a finite system of like fermions are described in terms of four-body correlated structures (quartets). These are real superpositions of products of two pairs of…

The sequence of ground state energy density at finite size, e_{L}, provides much more information than usually believed. Having at disposal e_{L} for short lattice sizes, we show how to re-construct an approximate quasi-particle dispersion…

We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…

We consider a many body fermionic system with an incommensurate external potential and a short range interaction in one dimension. We prove that, for certain densities and weak interactions, the zero temperature thermodynamical correlations…

We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of $N$ Majorana…

We present an algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest. Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of…

We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest…

We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node…

We investigate the non-equilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the $q\rightarrow\infty$ limit, where $q/2$ denotes the order of the random Dirac fermion interaction. We extend previous results by Eberlein et al.…

We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS_4 x CP^3. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute…

We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when…

The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…