Density matrix renormalization group approach to a two-dimensional bosonic model
نویسنده
چکیده
Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional λφ model to study spontaneous breakdown of discrete Z2 symmetry numerically. We obtain the critical coupling (λ/μ 2)c = 59.89 ± 0.01 and the critical exponent β = 0.1264 ± 0.0073, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limit with lattice sizes L = 250, 500, and 1000. We show that the lattice size L = 500 is sufficiently close to the the limit L → ∞ [1].
منابع مشابه
Time-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملDensity Matrices for a Chain of Oscillators
We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from ...
متن کاملA numerical renormalization group approach for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators
Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...
متن کاملNumerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model.
We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectra...
متن کاملTensor Product Variational Formulation for Quantum Systems
We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group m...
متن کامل