Nonvariational calculation of the relativistic and finite-size corrections for the helium ground state

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.

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

Modern Physics Letters B ◽

10.1142/s0217984916300076 ◽

2016 ◽

Vol 30 (25) ◽

pp. 1630007 ◽

Cited By ~ 2

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.

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

Modern Physics Letters B ◽

10.1142/s0217984912501345 ◽

2012 ◽

Vol 26 (21) ◽

pp. 1250134 ◽

Cited By ~ 3

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979297000575 ◽

1997 ◽

Vol 11 (09) ◽

pp. 1137-1151 ◽

Cited By ~ 9

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.

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FINITE SIZE CORRECTIONS FOR MULTIPARTICLE SPIN-½ NONLINEAR SCHRÖDINGER MODEL

Modern Physics Letters B ◽

10.1142/s021798499100191x ◽

1991 ◽

Vol 05 (23) ◽

pp. 1603-1606

Author(s):

YI-MIN LIU ◽

FU-CHO PU ◽

HANG SU

Keyword(s):

Critical Point ◽

Ground State ◽

Finite Size ◽

Conformal Anomaly ◽

Nonlinear Schrödinger ◽

Size Correction ◽

Finite Size Correction ◽

Finite Size Corrections ◽

Maclaurin Formula

Applied Euler-Maclaurin formula, we compute the finite size correction to the energy of the ground state for the Spin-½ Nonlinear Schrödinger model. We get conformal anomaly for this model at the critical point (T=0).

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