scholarly journals Many-body localization of spinless fermions with attractive interactions in one dimension

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Sheng-Hsuan Lin ◽  
Björn Sbierski ◽  
Florian Dorfner ◽  
Christoph Karrasch ◽  
Fabian Heidrich-Meisner
Keyword(s):  
Phase Diagram ◽  
Energy Density ◽  
Ground State ◽  
Intermediate Phase ◽  
Particle Density ◽  
Luttinger Liquid ◽  
Finite Size ◽  
Finite Energy ◽  
One Dimension ◽  
Many Body

We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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 COMPETING PHASES IN SPIN-½ J1-J2 CHAIN WITH EASY-PLANE ANISOTROPY

2011 ◽  
Vol 25 (12n13) ◽  
pp. 901-908 ◽  
Author(s):  
MASAHIRO SATO ◽  
SHUNSUKE FURUKAWA ◽  
SHIGEKI ONODA ◽  
AKIRA FURUSAKI
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Nearest Neighbor ◽  
Luttinger Liquid ◽  
Rich Variety ◽  
Narrow Region ◽  
Chiral Phases ◽  
Liquid Phases ◽  
Plane Anisotropy ◽  
Xxz Chain

We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly concerned with the case of ferromagnetic J1, and the case of antiferromagnetic J1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J1/J2 versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga–Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J1 side.

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 Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

Ground state of an Ising-type spin-1/2 chain with competing interactions

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1581-1585 ◽  
Author(s):  
T Tonegawa ◽  
H Matsumoto ◽  
T Hikihara ◽  
M Kaburagi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Nearest Neighbor ◽  
Intermediate Phase ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Competing Interactions ◽  
Density Matrix Renormalization ◽  
Diagonalization Method ◽  
Exact Diagonalization Method

The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = – Σi h2i–1,2i – J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 [Formula: see text] 0, J2 [Formula: see text] 0, and 1 > γ [Formula: see text] 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40Mg

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