Computing Masses from Effective Transfer Matrices

We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the approach we study the spectrum of large arrays of coupled quantum Ising chains. We demonstrate explicitly that the method can treat the various regimes of chains, in particular the three dimensional Ising ordering transition the chains undergo ...

We explain the recent numerical successes obtained by Tao Xiang's group, who developed and applied Tensor Renormalization Group methods for the Ising model on square and cubic lattices, by the fact that their new truncation method sharply singles out a surprisingly small subspace of dimension two. We show that in the two-state approximation, their transformation can be handled analytically yielding a value 0.964 for the critical exponent nu much closer to the exact value 1 th...

We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors which are iteratively optimized by the use of the ``vertical density matrix'' formed by cutting the system along the transfer direction. This algorithm, which ...

We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of DMRG. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising ...

We propose a new fast numerical renormalization group method,the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfer matrices gives the densitymatrix. We formulate the CTMRG method as a renormalization of 2D classical models.

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.

We present a spectroscopy scheme for the lattice field theory by using tensor renormalization group method combining with the transfer matrix formalism. By using the scheme, we can not only compute the energy spectrum for the lattice theory but also determine quantum numbers of the energy eigenstates. Furthermore, wave function of the corresponding eigenstate can also be computed. The first step of the scheme is to coarse-grain the tensor network of a given lattice model by u...

The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations that target the lowest hundreds of states $\{E(N)\}$ at system size $N$ instead of the ground state. Progressively larger $N$ reaches $T < 0.05t$ in correlated models with electron transfer $t$ between first neighbors and bandwidth $4t$. T...

We analyse the eigenvalue structure of the replicated transfer matrix of one-dimensional disordered Ising models. In the limit of $n \rightarrow 0$ replicas, an infinite sequence of transfer matrices is found, each corresponding to a different irreducible representation (labelled by a positive integer $\rho$) of the permutation group. We show that the free energy can be calculated from the replica symmetric subspace ($\rho =0$). The other ``replica symmetry broken'' represent...

We present an extension of a framework for simulating single quasiparticle or collective excitations on top of strongly correlated quantum many-body ground states using infinite projected entangled pair states, a tensor network ansatz for two-dimensional wave functions in the thermodynamic limit. Our approach performs a systematic summation of locally perturbed states in order to obtain excited eigenstates localized in momentum space, using the corner transfer matrix method, ...