arXiv subjects

Nicholas Pomata

Publications and source records attributed to Nicholas Pomata.

6 recordsLinked to original sources

arXiv2021

Order, Disorder, and Transitions in Decorated AKLT States on Bethe Lattices

Returning to one of the original generalizations of the AKLT state, we extend prior analysis on the Bethe lattice (or Cayley tree) to a variant with a series of $n$ spin-1 decorations placed on each edge. The recurrence relations derived for this system demonstrate that such systems are critical for coordination numbers $z=3^{n+1}$, demonstrating order for greater and disorder for lesser coordination number. We then generalize further, effectively interpolating between systems with different values of $n$, using two realizations, one isotropic under local $SU(2)$ transformations and one anisotropic. Exact analysis of these recurrence relations allows us to deduce the location and behavior of order-disorder phase transitions for $z>4$.

cond-mat.stat-mech↗

arXiv2020

In search of a many-body mobility edge with matrix product states in a Generalized Aubry-Andr\'e model with interactions

We investigate the possibility of a many-body mobility edge in the generalized Aubry-Andr\'e (GAA) model with interactions using the Shift-Invert Matrix Product States (SIMPS) algorithm [Phys. Rev. Lett. 118, 017201 (2017)]. The non-interacting GAA model is a one-dimensional quasiperiodic model with a self-duality-induced mobility edge. To search for a many-body mobility edge in the interacting case, we exploit the advantages of SIMPS that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for some to converge. Our analysis indicates that the targeted states in the presence of the single-particle mobility edge match neither `MBL-like' fully-converged localized states nor the fully delocalized case where SIMPS fails to converge. We benchmark the algorithm's output both for parameters that give fully converged, `MBL-like' localized states and for delocalized parameters where SIMPS fails to converge. In the intermediate cases, where the parameters produce a single-particle mobility edge, we find many-body states that develop entropy oscillations as a function of cut position at larger bond dimensions. These oscillations at larger bond dimensions, which are also found in the fully-localized benchmark but not the fully-delocalized benchmark, occur both at the band edge and center and may indicate convergence to a non-thermal state (either localized or critical).

cond-mat.dis-nn↗

arXiv2020

The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped

Recently various 2D AKLT models have been shown to be gapped, including the one on the hexagonal lattice. Here we report on a non-trivial 3D AKLT model which consists of spin-2 entities on the diamond lattice sites and one single spin-1 entity between every neighboring spin-2 site. Although the nonzero gap problem for the uniformly spin-2 AKLT models on the diamond and square lattices is still open, we are able to establish the existence of the gap for two planar lattices, which we call the inscribed square lattice and the triangle-octagon lattice, respectively. So far, these latter two models are the only two uniformly spin-2 AKLT models that have a provable nonzero gap above the ground state. We also discuss some attempts in proving the gap existence on both the square and kagome lattices. In addition, we show that if one can solve a finite-size problem of a weighted AKLT Hamiltonian and if the gap is larger than certain threshold, then the model on the square lattice is gapped in the thermodynamic limit. The threshold of the gap scales inversely with the linear size of the finite-size problem.

cond-mat.str-el↗

arXiv2019

Demonstrating the AKLT spectral gap on 2D degree-3 lattices

We establish that the spin-3/2 AKLT model on the honeycomb has a nonzero spectral gap. We use the relation between the anticommutator of two projectors and their sum, and apply it to related AKLT projectors that occupy plaquettes or other extended regions. We analytically reduce the complexity in the resulting eigenvalue problem and use a Lanczos numerical method to show that the required inequality for the nonzero spectral gap holds. This approach is also successfuly applied to several other spin-3/2 AKLT models on degree-3 semiregular tilings, such as the square octagon, star and cross lattices, where the complexity is low enough that exact diagonalization can be used instead of the Lanczos method. In addition, we also close the previously open cases in the singly decorated honeycomb and square lattices.

cond-mat.stat-mech↗

arXiv2019

AKLT models on decorated square lattices are gapped

The nonzero spectral gap of the original two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) models has remained unproven for more than three decades. Recently, Abdul-Rahman et al. [arXiv:1901.09297] provided an elegant approach and proved analytically the existence of a nonzero spectral gap for the AKLT models on the decorated honeycomb lattice (for the number $n$ of spin-1 decorated sites on each original edge no less than 3). We perform calculations for the decorated square lattice and show that the corresponding AKLT models are gapped if $n\ge 4$. Combining both results, we also show that a family of decorated hybrid AKLT models, whose underlying lattice is of mixed vertex degrees 3 and 4, are also gapped for $n\ge 4$. We develop a numerical approach that extends beyond what was accessible previously. Our numerical results further improve the nonzero gap to $n\ge 2$, including the establishment of the gap for $n=2$ in the decorated triangular and cubic lattices. The latter case is interesting, as this shows the AKLT states on the decorated cubic lattices are not Néel ordered, in contrast to the state on the undecorated cubic lattice.

quant-ph↗

arXiv2018

Phase transitions of a 2D deformed-AKLT model

We study spin-2 deformed-AKLT models on the square lattice, specifically a two-parameter family of $O(2)$-symmetric ground-state wavefunctions as defined by Niggemann, Klümper, and Zittartz, who found previously that the phase diagram consists of a Néel-ordered phase and a disordered phase which contains the AKLT point. Using tensor-network methods, we not only confirm the Néel phase but also find an XY phase with quasi-long-range order and a region adjacent to it, within the AKLT phase, with very large correlation length, and investigate the consequences of a perfectly factorizable point at the corner of that phase.

cond-mat.str-el↗