相关论文: Lefschetz Thimbles and Quantum Phases in Zero-Dime…
The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share…
Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from…
In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two…
In this talk I review the proposal to formulate quantum field theories (QFTs) on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations of lattice QFTs affected by sign problem. First I will review the theoretical…
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…
We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo…
Non-perturbative lattice QCD calculations at non vanishing baryon number density are hampered by the QCD sign problem. The path integral, that in lattice QCD is calculated numerically, becomes highly oscillating. One possible solution is…
We study the isotropic Heisenberg chain with nearest and next-nearest neighbour interactions. The ground state phase diagram is constructed in dependence on the additonal interactions and an external magnetic field. The thermodynamics is…
We study the zero-temperature phase diagram of the Lechner-Hauke-Zoller model. An analytic expression for the free-energy and critical coefficients for finite-size systems and in the thermodynamic limit are derived and numerically verified.…
In this work it is shown that dynamical quantum phase transitions in Loschmidt echos control the nonequilibrium dynamics of the order parameter after particular quantum quenches in systems with broken-symmetry phases. A direct connection…
We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show…
We apply the Lefschetz thimble formulation of field theories to a couple of different problems. We first address the solution of a complex 0-dimensional phi^4 theory. Although very simple, this toy-model makes us appreciate a few key issues…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
Zero-dimensional $O(n)$-symmetric sigma models are studied by using Picard--Lefschetz integration method in the presence of small symmetry-breaking perturbations. Due to approximate symmetry, downward flows turn out to show significant…
The phase diagram of a coupled tetrahedral Heisenberg model is obtained. The quantum chain has a local gauge symmetry and its eigenspectrum is obtained by the composition of the eigenspectra of spin-1/2 XXZ chains with arbitrary…
The quantum Lefschetz formula explains how virtual fundamental classes (or structure sheaves) of moduli stacks of stable maps behave when passing from an ambient target scheme to the zero locus of a section. It is only valid under special…
We investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact…
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of…
The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at…