Lower bounds for the ground-state energies of the two-dimensional Hubbard andt-Jmodels

1991 ◽  
Vol 43 (16) ◽  
pp. 13743-13746 ◽  
Author(s):  
Roser Valent ◽  
Joachim Stolze ◽  
P. J. Hirschfeld
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Two Dimensional ◽  
Ground State Energies

Calculation of ground-state energies of muonic molecules of hydrogen isotopes confined to a two-dimensional region

1990 ◽  
Vol 41 (7) ◽  
pp. 4049-4051 ◽  
Author(s):  
I. C. da Cunha Lima ◽  
M. Fabbri ◽  
A. Ferreira da Silva ◽  
A. Troper
Keyword(s):  
Ground State ◽  
Hydrogen Isotopes ◽  
Two Dimensional ◽  
Ground State Energies

scholarly journals Remarks on the boundary set of spectral equipartitions

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120492 ◽  
Author(s):  
P. Bérard ◽  
B. Helffer
Keyword(s):  
Riemannian Manifold ◽  
Lower Bound ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Two Dimensional ◽  
Nodal Sets ◽  
Nodal Domains ◽  
Open Set ◽  
Ground State Energies

Given a bounded open set in (or in a Riemannian manifold), and a partition of Ω by k open sets ω j , we consider the quantity , where λ ( ω j ) is the ground state energy of the Dirichlet realization of the Laplacian in ω j . We denote by ℒ k ( Ω ) the infimum of over all k -partitions. A minimal k -partition is a partition that realizes the infimum. Although the analysis of minimal k -partitions is rather standard when k =2 (we find the nodal domains of a second eigenfunction), the analysis for higher values of k becomes non-trivial and quite interesting. Minimal partitions are in particular spectral equipartitions, i.e. the ground state energies λ ( ω j ) are all equal. The purpose of this paper is to revisit various properties of nodal sets, and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We prove a lower bound for the length of the boundary set of a partition in the two-dimensional situation. We consider estimates involving the cardinality of the partition.

Analytic energies and wave functions of the two-dimensional Schrödinger equation: ground state of two-dimensional quartic potential and classification of solutions

2012 ◽  
Vol 90 (6) ◽  
pp. 503-513 ◽  
Author(s):  
Vladimír Tichý ◽  
Aleš Antonín Kuběna ◽  
Lubomír Skála
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
Quartic Potential ◽  
Ground State Energies ◽  
Fourth Order Polynomial

New analytic solutions of the two-dimensional Schrödinger equation with a two-dimensional fourth-order polynomial (i.e., quartic) potential are derived and discussed. The solutions represent the ground state energies and the corresponding wave functions. In general, the obtained results cannot be reduced to two one-dimensional cases.

scholarly journals Abelian and non-abelian symmetries in infinite projected entangled pair states

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Claudius Hubig
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Ground State ◽  
Heisenberg Model ◽  
Computational Effort ◽  
Square Lattice ◽  
Two Dimensional ◽  
Computational Speed ◽  
Speed Up ◽  
Ground State Energies

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions D=10D=10 in the square lattice Heisenberg model at computational effort comparable to calculations at D=6D=6 without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

Converging upper and lower bounds for ground-state energies of atomic nuclei

2005 ◽  
Vol 25 (3) ◽  
pp. 379-385
Author(s):  
G. P. Kamuntavičius ◽  
D. Germanas ◽  
R. K. Kalinauskas ◽  
S. Mickevičius ◽  
R. Žemaičinienė
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Upper And Lower Bounds ◽  
Atomic Nuclei ◽  
Ground State Energies

A procedure for obtaining lower bounds for ground state energies of atoms and molecules

1969 ◽  
Vol 13 (2) ◽  
pp. 155-158
Author(s):  
M. Bersohn ◽  
M. Glicksohn ◽  
J. Stewart
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Atoms And Molecules ◽  
Ground State Energies
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