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Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
In this work we describe a new technique for numerical exact diagonalization. The method is particularly suitable for cold bosonic atoms in optical lattices, in which multiple atoms can occupy a lattice site. We describe the use of the…
The classical and quantum simulation of lattice gauge theories (LGTs) with Lie groups is hindered by the infinite-dimensional Hilbert space of gauge degrees of freedom. In a recent work [Phys. Rev. X 15, 031065 (2025)], we introduced a new…
We present two-loop renormalization of $\phi^3$-model effective action by using the background field method and cutoff momentum regularization. In this paper, we also study a derivation of the quantum equation of motion and its application…
We develop a method for computing exact one-loop quantum corrections to the energies of static classical backgrounds in renormalizable quantum field theories. We use a continuum density of states formalism to construct a regularized Casimir…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories. Impressive as this is, one would rather…
We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…
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,…
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique…
We present a renormalization scheme which simplifies the dynamics of an important class of interacting multi-qubit systems. We show that a wide class of M+1 qubit systems can be reduced to an equivalent n+1 qubit system with n equal to, or…
Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model…
The excitation by a high frequency field of multi--level quantum systems with a slowly varying density of states is investigated. A general approach to study such systems is presented. The Floquet eigenstates are characterized on several…
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the…
At strong on-site repulsion $ U $, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected…