相关论文: Monte Carlo Hamiltonian: Generalization to Quantum…
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we…
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…
In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In…
We present a new way to compute thermodynamical observables on the lattice. We compute excited states and thermodynamical functions in the scalar model via the Monte Carlo Hamiltonian technique. We find agreement with standard Lagrangian…
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum…
We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.
In order to extend the recently proposed Monte Carlo Hamiltonian to many-body systems, we suggest to concept of a stochastic basis. We apply it to the chain of $N_s=9$ coupled anharmonic oscillators. We compute the spectrum of excited…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some…
We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis.…
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by…
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic…
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called…
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…
Quantum Monte Carlo methods are first-principle approaches that approximately solve the Schr\"odinger equation stochastically. As compared to traditional quantum chemistry methods, they offer important advantages such as the ability to…
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 propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…