The $t$ -expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities ${M}_{n}(t)$ and ${D}_{n}(t)$ which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard $t$ -expansion, the $t$ -series for ${M}_{n}(t)$ and ${D}_{n}(t)$ are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.The $t$-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities ${M}_{n}(t)$ and ${D}_{n}(t)$ which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard $t$-expansion, the $t$-series for ${M}_{n}(t)$ and ${D}_{n}(t)$ are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsOct 15, 19909 citations

Two-dimensional XXZ model ground-state properties using an analytic Lanczos expansion

Nicholas S. Witte, Lloyd C. L. Hollenberg, Zheng Weihong

We develop a formalism for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using an analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground-state energies. The ground-state energy, staggered magnetization, and excited state gap of the two-dimensional anisotropic antiferromagnetic Heisenberg model are then calculated using this expansion for a range of anisotropy parameters, and compared to other moment-based techniques, such as the t expansion, and spin-wave theory, and series-expansion methods. We find that far from the isotropic point all moment methods give essentially very similar results, but near the isotropic point the plaquette expansion is generally better than the others.We develop a formalism for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using an analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground-state energies. The ground-state energy, staggered magnetization, and excited state gap of the two-dimensional anisotropic antiferromagnetic Heisenberg model are then calculated using this expansion for a range of anisotropy parameters, and compared to other moment-based techniques, such as the t expansion, and spin-wave theory, and series-expansion methods. We find that far from the isotropic point all moment methods give essentially very similar results, but near the isotropic point the plaquette expansion is generally better than the others.

arXiv:cond-mat/9702017Physical review. B, Condensed matterApr 15, 199716 citations

Excited states in finite systems

WORLD SCIENTIFIC eBooksMay 1, 20080 citations

Excited states in finite systems

WORLD SCIENTIFIC eBooksOct 13, 20250 citations

Exact finite volume expectation values of local operators in excited states

Balázs Pozsgay, István M. Szécsényi, G. Takács

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

arXiv:1412.8436Journal of High Energy PhysicsApr 1, 201517 citations

The

t

-expansion method for calculating ground-state energies of Hamiltonian systems is generalized to excited states. We introduce quantities

{M}_{n}(t)

and

{D}_{n}(t)

which for $t\ensuremath{\rightarrow}\ensuremath{\infty}$ converge to ${\ensuremath{\Sigma}}_{n}={E}_{0}+{E}_{1}+\dots{}+{E}_{n}$ and ${\ensuremath{\Delta}}_{n}={E}_{n+1}\ensuremath{-}{E}_{n}$, respectively. Like in the standard

t

-expansion, the

t

-series for

{M}_{n}(t)

and

{D}_{n}(t)

are constructed from moments of the Hamiltonian. The values of ${\ensuremath{\Sigma}}_{n}$ and ${\ensuremath{\Delta}}_{n}$ can then be estimated using (e.g.) a generalization of the connected-moment expansion of Cioslowski.