Related papers: Perturbational Decomposition Analysis for Quantum …
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a…
We investigate the quantum dynamics of the transverse field Ising model on the triangular lattice through large-scale quantum Monte Carlo simulations and stochastic analytic continuation. At weak transverse field, we capture for the first…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian…
We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to $16 \times 16$ spins. In the ordered phase, the model is predicted to exhibit dynamically constrained dynamics, leading to confinement of…
Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle…
In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be…
Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more…
The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose…
We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
When looking for analytical approaches to treat frustrated quantum magnets, it is often very useful to start from a limit where the ground state is highly degenerate. This chapter discusses several ways of deriving {effective Hamiltonians}…
We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter…
The integrated perturbation theory (iPT) is a set of methods in nonlinear perturbation theory for the structure formation in the Universe. In Papers I and II [arXiv:2210.10435, arXiv:2210.11085], the basic formalism and technical methods of…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
Ground state of the one-dimensional transverse field Ising model is investigated under the hyperbolic deformation, where the energy scale of j-th bond is proportional to the function \cosh ( j \lambda ) that contains a parameter \lambda.…
We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain with a strong, on-site $\mathbb{Z}_2$ symmetry. While the steady-state of this evolution is…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time…