Lecture notes in physics. M, Monographs

Hamiltonian Representation

Published Jan 1, 1994• 0 citations

DOI: 10.1007/978-3-540-48651-0_4

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Lecture notes in physics. M, Monographs

Hamiltonian Representation

Published Jan 1, 1994• 0 citations

Publisher

DOI: 10.1007/978-3-540-48651-0_4

Related papers

MODEL HAMILTONIANS

WORLD SCIENTIFIC eBooksNov 1, 19900 citations

BOSONIC OPERATOR HAMILTONIAN MODELS OF JOSEPHSON JUNCTIONS IN SERIES AND IN PARALLEL AND THEIR PROJECTIONS ONTO ENTANGLED STATE REPRESENTATIONS

WAN-YU YE, Hong-Yi Fan

Modern Physics Letters BJun 10, 20071 citation

Cyclic representations of the periodic Temperley–Lieb algebra, complex Virasoro representations and stochastic processes

Francisco Castilho Alcaraz, Arun Ram, V. Rittenberg

An $N$ ${L} \choose {L/2}$ -dimensional representation of the periodic Temperley-Lieb algebra $TL_L(x)$ is presented. It is also a representation of the cyclic group $Z_N$ . We choose $x = 1$ and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamiltonian contains representations of the Virasoro algebra with complex highest weights. The $N = 3$ case is discussed in detail. One discusses shortly the consequences of the existence of complex Virasoro representations on the physical properties of the systems.An $N$ ${L} \choose {L/2}$-dimensional representation of the periodic Temperley-Lieb algebra $TL_L(x)$ is presented. It is also a representation of the cyclic group $Z_N$. We choose $x = 1$ and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamiltonian contains representations of the Virasoro algebra with complex highest weights. The $N = 3$ case is discussed in detail. One discusses shortly the consequences of the existence of complex Virasoro representations on the physical properties of the systems.

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arXiv:cond-mat/9903159Mar 10, 19990 citations

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Springer eBooksJan 1, 19850 citations

N

{L} \choose {L/2}

-dimensional representation of the periodic Temperley-Lieb algebra

TL_L(x)

is presented. It is also a representation of the cyclic group

Z_N

. We choose

x = 1

and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamiltonian contains representations of the Virasoro algebra with complex highest weights. The

N = 3

case is discussed in detail. One discusses shortly the consequences of the existence of complex Virasoro representations on the physical properties of the systems.

We present functional Schrödinger representations of Holstein-Primakoff boson and slave-boson theories for the Heisenberg Hamiltonian and the

t-J

Hamiltonian respectively. Based on these representations we obtain the dispersion relations of magnons for two dimensional antiferromagnets. By applying the functional Schrödinger representation of the Holstein-Primakoff boson theory to the Heisenberg Hamiltonian, the exchange energy is correctly predicted and the self-energy of quasi-hole is obtained. From the use of the functional Schrödinger representation of the

t-J

Hamiltonian it is shown that at half-filling the dispersion relation obtained from the slave-boson theory leads to that obtained from the Holstein-Primakoff boson approach.