scholarly journals Gapped PVBS models for all species numbers and dimensions

2019 ◽  
Vol 31 (09) ◽  
pp. 1950028 ◽  
Author(s):  
Marius Lemm ◽  
Bruno Nachtergaele
Keyword(s):  
Ground State ◽  
Spectral Gap ◽  
Arbitrary Dimension ◽  
Finite Size ◽  
Spin Model ◽  
Species Number ◽  
Martingale Method ◽  
State Sector ◽  
Dimension Formula ◽  
Boundary States

Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature [Formula: see text] particle species on [Formula: see text]. The PVBS models were originally introduced as toy models for the classification of ground state phases. A crucial ingredient for this classification is the existence of a spectral gap above the ground state sector. In this work, we derive a spectral gap for PVBS models at arbitrary species number [Formula: see text] and in arbitrary dimension [Formula: see text] in the perturbative regime of small anisotropy parameters. Instead of using the more common martingale method, the proof verifies a finite-size criterion in the spirit of Knabe.

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.

KINETIC RESPONSE OF SURFACES DEFINED BY FINITE FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (04) ◽  
pp. 461-476 ◽  
Author(s):  
PRADEEP R. NAIR ◽  
MUHAMMAD A. ALAM
Keyword(s):  
Scaling Laws ◽  
Finite Size ◽  
Critical Dimension ◽  
The Novel ◽  
Scale Invariant ◽  
Fractal Surfaces ◽  
Dimension Formula ◽  
Diffusion Limited ◽  
Engineered Systems ◽  
Size Limits

Historically, fractal analysis has been remarkably successful in describing wide ranging kinetic processes on (idealized) scale invariant objects in terms of elegantly simple universal scaling laws. However, as nanostructured materials find increasing applications in energy storage, energy conversion, healthcare, etc., one must reexamine the premise of traditional fractal scaling laws as it only applies to physically unrealistic infinite systems, while all natural/engineered systems are necessarily finite. In this article, we address the consequences of the 'finite-size' problem in the context of time dependent diffusion towards fractal surfaces via the novel technique of Cantor-transforms to (i) illustrate how finiteness modifies its classical scaling exponents; (ii) establish that for finite systems, the diffusion-limited reaction is decelerated below a critical dimension [Formula: see text] and accelerated above it; and (iii) to identify the crossover size-limits beyond which a finite system can be considered (practically) infinite and redefine the very notion of 'finiteness' of fractals in terms of its kinetic response. Our results have broad implications regarding dynamics of systems defined by the same fractal dimension, but differentiated by degree of scaling iteration or morphogenesis, e.g. variation in lung capacity between a child and adult.

scholarly journals Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

scholarly journals Dimer description of the SU(4) antiferromagnet on the triangular lattice

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Anna Keselman ◽  
Lucile Savary ◽  
Leon Balents
Keyword(s):  
Phase Diagram ◽  
Triangular Lattice ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Spin Model ◽  
Translation Invariance ◽  
Multilayer Graphene ◽  
High Symmetry ◽  
Starting Point

In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.

scholarly journals Irreversible work versus fidelity susceptibility for infinitesimal quenches

2017 ◽  
Vol 31 (06) ◽  
pp. 1750065 ◽  
Author(s):  
Simone Paganelli ◽  
Tony J. G. Apollaro
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Ground State ◽  
Finite Size ◽  
Scaling Relations ◽  
Zero Temperature ◽  
Finite Size Scaling ◽  
Ising Chain ◽  
Extra Term ◽  
Explicit Relation

We compare the irreversible work produced in an infinitesimal sudden quench of a quantum system at zero temperature with its ground state fidelity susceptibility, giving an explicit relation between the two quantities. We find that the former is proportional to the latter but for an extra term appearing in the irreversible work which includes also contributions from the excited states. We calculate explicitly the two quantities in the case of the quantum Ising chain, showing that at criticality they exhibit different scaling behaviors. The irreversible work, rescaled by square of the quench’s amplitude, exhibits a divergence slower than that of the fidelity susceptibility. As a consequence, the two quantities obey also different finite-size scaling relations.

scholarly journals Geometries and Electronic States of Divacancy Defect in Finite-Size Hexagonal Graphene Flakes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Lili Liu ◽  
Shimou Chen
Keyword(s):  
Ground State ◽  
First Principles ◽  
Density Functional ◽  
Singlet State ◽  
Tight Binding ◽  
Finite Size ◽  
Electronic States ◽  
Closed Shell ◽  
Graphene Flakes ◽  
Self Consistent

The geometries and electronic properties of divacancies with two kinds of structures were investigated by the first-principles (U) B3LYP/STO-3G and self-consistent-charge density-functional tight-binding (SCC-DFTB) method. Different from the reported understanding of these properties of divacancy in graphene and carbon nanotubes, it was found that the ground state of the divacancy with 585 configurations is closed shell singlet state and much more stable than the 555777 configurations in the smaller graphene flakes, which is preferred to triplet state. But when the sizes of the graphene become larger, the 555777 defects will be more stable. In addition, the spin density properties of the both configurations are studied in this paper.

scholarly journals Infinite series of quaternionic 1-vertex cube complexes, the doubling construction, and explicit cubical Ramanujan complexes

2019 ◽  
Vol 29 (06) ◽  
pp. 951-1007
Author(s):  
Nithi Rungtanapirom ◽  
Jakob Stix ◽  
Alina Vdovina
Keyword(s):  
Arbitrary Dimension ◽  
Congruence Subgroups ◽  
Quaternion Algebras ◽  
Ramanujan Graphs ◽  
Dimension Formula ◽  
Cubical Sets ◽  
Higher Dimensional ◽  
Residually Finite Groups ◽  
Doubling Construction ◽  
Effective Use

We construct vertex transitive lattices on products of trees of arbitrary dimension [Formula: see text] based on quaternion algebras over global fields with exactly two ramified places. Starting from arithmetic examples, we find non-residually finite groups generalizing earlier results of Wise, Burger and Mozes to higher dimension. We make effective use of the combinatorial language of cubical sets and the doubling construction generalized to arbitrary dimension. Congruence subgroups of these quaternion lattices yield explicit cubical Ramanujan complexes, a higher-dimensional cubical version of Ramanujan graphs (optimal expanders).

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.

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