The conventional renormalization-group analysis of the tricritical behavior of a metamagnet is completed by a description of the first-order transition below the tricritical temperature, and the conditions for the discontinuity in the magnetization are explicitly verified in an Ising spin model. The singularity structure of the crossover scaling function is derived from relations between the scaling fields for the critical and tricritical fixed points. Numerical calculations illustrating various aspects of the theory are given for a square-lattice Ising model in a four-cell cluster approximation.The conventional renormalization-group analysis of the tricritical behavior of a metamagnet is completed by a description of the first-order transition below the tricritical temperature, and the conditions for the discontinuity in the magnetization are explicitly verified in an Ising spin model. The singularity structure of the crossover scaling function is derived from relations between the scaling fields for the critical and tricritical fixed points. Numerical calculations illustrating various aspects of the theory are given for a square-lattice Ising model in a four-cell cluster approximation.

Physical review. B, Solid stateMar 1, 197649 citations

Symmetry adapted finite-cluster solver for quantum Heisenberg model in two dimensions: a real-space renormalization approach

Vl. E. Sinitsyn, Irina Gennad'evna Bostrem, Alexander S. Ovchinnikov

We present a quantum cluster solver for the spin- S Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and non-Abelian SU (2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice, and a calculation of local observables is demonstrated. A symmetry-based truncation procedure is suggested and verified numerically.We present a quantum cluster solver for the spin- S Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and non-Abelian SU (2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice, and a calculation of local observables is demonstrated. A symmetry-based truncation procedure is suggested and verified numerically.

arXiv:cond-mat/0612350Journal of Physics A Mathematical and TheoreticalJan 9, 200714 citations

Numerical Renormalization Group Methods

Simone Montangero

Springer eBooksJan 1, 20180 citations

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

Trithep Devakul, Satya N. Majumdar, David A. Huse

We calculate the probability distribution of entanglement entropy $S$ across a cut of a finite one-dimensional spin chain of length $L$ at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L)\ensuremath{\sim}{L}^{\ensuremath{-}\ensuremath{\psi}(k)}$, where $k\ensuremath{\equiv}S/ln\left[L/{L}_{0}\right]$, the large deviation function $\ensuremath{\psi}(k)$ is found explicitly, and ${L}_{0}$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large $L$ via a mapping to Majorana fermions.We calculate the probability distribution of entanglement entropy $S$ across a cut of a finite one-dimensional spin chain of length $L$ at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L)\ensuremath{\sim}{L}^{\ensuremath{-}\ensuremath{\psi}(k)}$, where $k\ensuremath{\equiv}S/ln\left[L/{L}_{0}\right]$, the large deviation function $\ensuremath{\psi}(k)$ is found explicitly, and ${L}_{0}$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large $L$ via a mapping to Majorana fermions.

arXiv:1612.02012Physical review. B./Physical review. BMar 20, 201714 citations

Renormalization group methods

Kenneth Geddes Wilson

Advances in MathematicsMay 1, 197574 citations

We calculate the probability distribution of entanglement entropy

S

across a cut of a finite one-dimensional spin chain of length

L

at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L)\ensuremath{\sim}{L}^{\ensuremath{-}\ensuremath{\psi}(k)}$, where $k\ensuremath{\equiv}S/ln\left[L/{L}_{0}\right]$, the large deviation function $\ensuremath{\psi}(k)$ is found explicitly, and

{L}_{0}

is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large

L

via a mapping to Majorana fermions.