相关论文: Fermion-bag inspired Hamiltonian lattice field the…

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions…

We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a…

Two formidable bottlenecks to the applicability of QMC include: (1) the sign problem and (2) algorithmic update inefficiencies. In this thesis, I overcome both these difficulties for a class of problems by extending the fermion bag approach…

The recently proposed fermion bag approach is a powerful technique to solve some four-fermion lattice field theories. Due to the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo…

The fermion bag is a powerful idea that helps to solve fermion lattice field theories using Monte Carlo methods. Some sign problems that had remained unsolved earlier can be solved within this framework. In this work we argue that the…

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$…

Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is studied in 1+1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair…

Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge…

By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…

We construct a fermionic lattice model containing interacting spin-$\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by…

We investigate the real-time dynamics of U(1) and SU(N) gauge theories coupled to fermions on a lattice. While real-time lattice gauge theory is not amenable to standard importance sampling techniques, for a large class of time-dependent…

Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…

Unlike the fundamental forces of the Standard Model the quantum effects of gravity are still experimentally inaccessible. Rather surprisingly quantum aspects of gravity, such as massive gravitons, can emerge in experiments with fractional…

Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the…

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…

Quantum phase transitions driven by electronic correlations are central to understanding the physics of graphene and related two-dimensional materials. A paradigmatic example is the semimetal-to-Mott-insulator transition on the honeycomb…

Relativistic fermionic field theories constitute the fundamental description of all observable matter. The simplest of the models provide a useful, classically verifiable benchmark for noisy intermediate scale quantum computers. We…

We study relativistic fermions in three euclidean dimensions with four- and six-fermion interactions of the Gross-Neveu type. In the limit of many fermion flavors, and besides the isolated free fixed point, the theory displays a line of…

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…