Finite-Size Corrections in the Supersymmetric t–J Model with Boundary Fields

1997 ◽  
Vol 11 (09) ◽  
pp. 1137-1151 ◽  
Author(s):  
Hitoshi Asakawa ◽  
Masuo Suzuki
Keyword(s):  
Ground State ◽  
State Energy ◽  
Present Model ◽  
Scaling Limit ◽  
Finite Size ◽  
Partition Functions ◽  
Excitation Energies ◽  
Ground State Degeneracy ◽  
Boundary Fields ◽  
Finite Size Corrections

The supersymmetric t–J model with boundary fields is discussed. Using the exact solution of the present model, the finite-size corrections of the ground-state energy and the low-lying excitation energies are calculated. The partition functions are evaluated in the scaling limit to obtain the conformal weights of the primary fields in the present model. A surface critical exponent and the ground-state degeneracy are also derived.

Mixture of interacting supersymmetric spinless fermions and bosons in a one-dimensional trap

2016 ◽  
Vol 30 (25) ◽  
pp. 1630007 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Gas Phase ◽  
Ground State ◽  
State Energy ◽  
Optical Trap ◽  
Interaction Strength ◽  
Finite Size ◽  
One Dimension ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
Finite Size Corrections

We consider a gas mixture consisting of spinless fermions and bosons in one dimension interacting via a repulsive [Formula: see text]-function potential. Bosons and fermions are assumed to have equal masses and the interaction strength between bosons and among bosons and fermions is the same. Using the Bethe ansatz solution of the model, we study the ground state properties, the dressed energy potentials for the two bands of rapidities, the elementary particle and hole excitations, the thermodynamics, the finite size corrections to the ground state energy leading to the conformal towers, and the asymptotic behavior at large distances of some relevant correlation functions. The low-energy excitations of the system form a two-component Luttinger liquid. In an elongated optical trap the gas phase separates as a function of the distance from the center of the trap.

scholarly journals Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Finite Lattices ◽  
Antiferromagnetic Ising Model ◽  
Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

GROUND STATE OF THE 2D EXTENDED HUBBARD MODEL WITH MORE THAN NEAREST-NEIGHBOR INTERACTIONS

2012 ◽  
Vol 26 (29) ◽  
pp. 1250156 ◽  
Author(s):  
S. HARIR ◽  
M. BENNAI ◽  
Y. BOUGHALEB
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
Eigenvalues And Eigenvectors ◽  
Repulsion Energy

We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.

scholarly journals Motions of the String Solutions in the XXZ Spin Chain Under a Varying Twist

1997 ◽  
Vol 12 (04) ◽  
pp. 801-838 ◽  
Author(s):  
N. Fumita ◽  
H. Itoyama ◽  
T. Oota
Keyword(s):  
Ground State ◽  
Spin Chain ◽  
Imaginary Axis ◽  
Berry Phase ◽  
Numerical Study ◽  
Twist Angle ◽  
Finite Size ◽  
Bound State ◽  
Branch Points ◽  
Finite Size Corrections

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study in a finite size system. In the attractive critical regime 0 < Δ < 1, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of n-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase in the regime Δ ≤ -1 also, establishing the continuity of the previous results at -1 < Δ < 0 to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle (or the bound state) involved in the process.

GROUND STATES IN THREE-DIMENSIONAL ±J EDWARDS–ANDERSON SPIN GLASSES WITH FREE BOUNDARIES

2000 ◽  
Vol 11 (03) ◽  
pp. 589-592
Author(s):  
FRAUKE LIERS ◽  
MICHAEL JÜNGER
Keyword(s):  
Spin Glass ◽  
Spin Glasses ◽  
State Energy ◽  
Infinite System ◽  
Three Dimensional ◽  
Finite Size ◽  
Ground States ◽  
Free Boundaries ◽  
Finite Size Corrections

By an exact calculation of the ground states for the ±J Edwards–Anderson spin glass, one can extrapolate the ground state energy to infinite system sizes. We calculate the exact ground states for the three-dimensional spin glass with free boundaries for system sizes up to 10 and fit different finite-size functions. We cannot decide, only from the quality of the fit, which fitting function to choose. Relying on the literature values for the extrapolated energy, we find the finite-size corrections to vary as 1/L.

scholarly journals FINITE SIZE EFFECTS IN ENTANGLED RINGS OF QUBITS

2004 ◽  
Vol 02 (02) ◽  
pp. 149-169 ◽  
Author(s):  
T. MEYER ◽  
U. V. POULSEN ◽  
K. ECKERT ◽  
M. LEWENSTEIN ◽  
D. BRUß
Keyword(s):  
Ground State ◽  
Size Effects ◽  
State Energy ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Spin Model ◽  
Total Spin ◽  
Finite Size Effects ◽  
Invariant Rings

We study translationally invariant rings of qubits with a finite number of sites N, and determine the maximal nearest-neighbor entanglement for a fixed z-component of the total spin. For small numbers of sites we present analytical results. We establish a relation between the maximal nearest-neighbor concurrence and the ground state energy of an XXZ spin model. This connection allows us to calculate the concurrence numerically for N≤24. We point out some interesting finite-size effects. Finally, we generalize our results beyond nearest neighbors.

DISORDERING OF THE CORRELATED STATE OF THE QUANTUM HALL BILAYER AT FILLING FACTOR ν = 1

2012 ◽  
Vol 26 (21) ◽  
pp. 1250134 ◽  
Author(s):  
Z. PAPIĆ ◽  
M. V. MILOVANOVIĆ
Keyword(s):  
Liquid Phase ◽  
Ground State ◽  
Fermi Liquid ◽  
Quantum Hall ◽  
Finite Size ◽  
Critical Distance ◽  
Fermi Liquids ◽  
Direct Transition ◽  
State Changes ◽  
Finite Size Corrections

The phase diagram of a quantum Hall bilayer at total filling ν = 1 contains an incompressible superfluid for small distances d between the layers, as well as the compressible phase corresponding to two uncoupled Fermi liquids for large d. Using exact diagonalization on the sphere and torus geometry, we investigate a long-standing question of the nature of the transition between the two regimes, and the possibility for the existence of a paired phase in the transition region. We find considerable evidence for a direct transition between the superfluid and the Fermi liquid phase, based in particular on the behavior of the ground state energy on the sphere (including appropriate finite-size corrections) as a function of d. At the critical distance dC ≈ 11.6ℓB the topological number ("shift") of the ground state changes, suggesting that tuning the layer separation d in experiment likely leads to a direct transition between the superfluid and the Fermi liquid phase.

scholarly journals The energy correction due to a finite size nucleus of the hydrogen atom confined in a penetrable spherical cavity

2018 ◽  
Vol 64 (4) ◽  
pp. 399
Author(s):  
Norberto Aquino ◽  
Alejandro Rojas ◽  
Henry Montgomery Jr.
Keyword(s):  
Hydrogen Atom ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Finite Size ◽  
Point Particle ◽  
Energy Correction ◽  
A Value ◽  
Free Hydrogen ◽  
Uniform Charge Distribution

We computed accurate values for the ground state energy of a hydrogen atom by a finite spherical barrier of height V0 as a function of the confinement radius . We consider the nucleus as a sphere with a uniform charge distribution instead of as a point particle. The contribution to the ground state energy due to the finite nuclear size is computed as a function of the confinement radius,  and the height of the barrier, V0, using time-independent perturbation theory. For an impenetrable cavity with .5 au, we found that this energy correction is fifty times higher than the corresponding value for the free hydrogen atom. For a finite value of V0,we found that the maximum of the energy correction is reached at a value  which very is close to the position at which the electron density is most compact around to the nucleus. This is confirmed though the Shannon entropy in configuration space.

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