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A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte-Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space…
We present a unified theory of the variational Monte Carlo (VMC) and determinant quantum Monte Carlo (DQMC) methods using a novel density matrix formulation of VMC. We introduce an efficient algorithm for VMC to compute correlation…
We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is…
We study thermodynamics of the 3D Hubbard model at half filling on approach to the N\'eel transition by means of large-scale unbiased Diagrammatic Determinant Monte Carlo simulations. We obtain the transition temperature in the strongly…
Conformal field theories in curved backgrounds have been used to describe inhomogeneous one-dimensional systems, such as quantum gases in trapping potentials and non-equilibrium spin chains. This approach provided, in a elegant and simple…
On the basis of quantum Monte Carlo (QMC) simulations we study the formation of Mott domains in the one-dimensional Hubbard model with an additional confining potential. We find evidences of quantum critical behavior at the boundaries of…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the R\'enyi…
The Hofstadter-Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moir\'e materials. Few large-scale, numerically exact simulations exists for…
Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open…
We investigate the performance and accuracy of digital quantum algorithms for the study of static and dynamic properties of the fermionic Hubbard model at half-filling with next-nearest neighbour hopping terms. We provide quantum circuits…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is…
Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…
Determinant quantum Monte Carlo (DQMC), formulated in complex-fermion representation, has played a key role in studying strongly-correlated fermion systems. However, its applicability is limited due to the requirement of particle-number…
Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method [Phys. Rev. Res. 2,…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
This thesis explores adaptive inference as a tool to characterize quantum systems using experimental data, with applications in sensing, calibration, control, and metrology. I propose and test algorithms for learning Hamiltonian and Kraus…
We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.