**Latest Papers in Condensed Matter Physics**

Statistical Mechanics

### The stability-limit conjecture revisited (1905.13745v1)

**Pheerawich Chitnelawong, Francesco Sciortino, Peter H. Poole**

*2019-05-31*

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region, and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this reentrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si.

### AKLT models on decorated square lattices are gapped (1905.01275v2)

**Nicholas Pomata, Tzu-Chieh Wei**

*2019-05-03*

Abdul-Rahman et al. in 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 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 . 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 . We develop a numerical approach that extends beyond what was accessible previously. Our numerical results further improve the nonzero gap to , including the establishment of the gap for 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 N'eel ordered, in contrast to the state on the un-decorated cubic lattice.

### Origin of the slow growth of entanglement entropy in long-range interacting systems (1811.05505v2)

**Alessio Lerose, Silvia Pappalardi**

*2018-11-13*

We unveil the general mechanism underlying the counterintuitive slowdown of entanglement entropy dynamics in long-range interacting systems, demonstrated by recent extensive numerical work. We focus on general quantum spin systems with slowly-decaying interactions and demonstrate that entanglement growth is primarily governed by the nonlinear semiclassical dynamics of collective degrees of freedom. We connect bipartite entanglement entropy dynamics with the time-dependent spin squeezing, and show how a universal logarithmic growth emerges in the absence of semiclassical chaos. All our analytical results agree with numerical computations for quantum Ising chains with long-range couplings. Our findings establish a novel viewpoint on entanglement production induced by long-range interactions, and are experimentally relevant for accessing entanglement in highly-controllable platforms, including trapped ions, atomic condensates, and cavity-QED systems.

### Conjectures about the ground state energy of the Lieb-Liniger model at weak repulsion (1905.13705v1)

**Zoran Ristivojevic**

*2019-05-31*

In this paper we develop an alternative description to solve the problem of ground state energy of the Lieb-Liniger model that describes one-dimensional bosons with contact repulsion. For this integrable model we express the Lieb integral equation in the representation of Chebyshev polynomials. The latter form is convenient to efficiently obtain very precise numerical results in the singular limit of weak interaction. Such highly precise data enables us to use the integer relation algorithm to discover the analytical form of the coefficients in the expansion of the ground state energy for small interaction parameter. We obtained the first nine terms of the expansion using quite moderate numerical efforts. The detailed knowledge of behavior of the ground state energy on the interaction immediately leads to the exact perturbative results for the excitation spectrum.

### Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions (1709.04483v6)

**Joshuah T. Heath, Kevin S. Bedell**

*2017-09-13*

We propose a closed form for the statistical distribution of non-interacting Majorana fermions at low temperature. Majorana particles often appear in the contemporary many-body literature in the Kitaev, Fu-Kane, or Sachdev-Ye-Kitaev models, where the Majorana condition of self-conjugacy immediately results in nonconserved particle number, non-trivial braiding statistics, and the absence of a noninteracting limit. We deviate from this description and instead consider a gas of noninteracting, spin-1/2 Majorana fermions that obey the spin-statistics theorem via imposing a condensed matter analog of momentum conservation. This allows us to build a quantum statistical theory of the Majorana system in the low temperature, low density limit without the need to account for strong fluctuations in the particle number. A combinatorial analysis leads to a configurational entropy which deviates from the fermionic result with an increasing number of available microstates. A number-conserving Majorana distribution function is derived which shows signatures of a sharply-defined Fermi surface at finite temperatures. Such a distribution is then re-derived from a microscopic model in the form of a modified Kitaev chain with a bosonic pair interaction. The thermodynamics of this free Majorana system is found to be nearly identical to that of a free Fermi gas, except now distinguished by a two-fold ground state degeneracy and, subsequently, a residual entropy at zero temperature. Despite clear differences with the anyonic or Sachdev-Ye-Kitaev models, we nevertheless find surprising agreement between our theory and experimental signatures of Majorana excitations in several materials. Experimental realization of our exactly solvable model is also discussed in the realm of astrophysical and high-energy phenomena.

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