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K. Damle

Publications and source records attributed to K. Damle.

10 recordsLinked to original sources
arXiv2021

Melting of three-sublattice order in triangular lattice Ising antiferromagnets: Power-law order, $Z_6$ parafermionic multicriticality, and weakly first order transitions

The nature of the thermal melting process by which triangular-lattice Ising antiferromagnets lose their low-temperature ferrimagnetic three-sublattice order depends on the range of the interactions: It changes character when second and third neighbour ferromagnetic interactions become comparable to the nearest-neighbour antiferromagnetic coupling. We present a detailed numerical characterization of the corresponding threshold at which two-step melting of three-sublattice order gives way to a direct first-order transition at which this order is lost. The multicritical behaviour at this threshold is argued to be in the universality class of the $Z_6$ parafermion conformal field theory with central charge $c=5/4$. The presence of this multicritical threshold influences the melting behaviour and long-wavelength properties over a fairly large range of parameters, and at temperatures that are of the same order as the exchange interactions. It is therefore of potential experimental relevance in the context of easy-axis triangular lattice antiferromagnets that display such low temperature ordering.

cond-mat.stat-mech↗
arXiv2021

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice

We study the phase diagram of a system of $2\times 2\times 1$ hard plates on the three dimensional cubic lattice, {\em i.e.} a lattice gas of plates that each cover an elementary plaquette of the cubic lattice and occupy its four vertices, with the constraint that no two plates occupy the same site of the cubic lattice. We focus on the isotropic system, with equal fugacities for the three orientations of plates. We show, using grand canonical Monte Carlo simulations, that the system undergoes two density-driven phase transitions with increasing density of plates: the first from a disordered fluid to a layered phase, and the second from the layered phase to a sublattice-ordered phase. In the layered phase, the system breaks up into disjoint slabs of thickness two along one spontaneously chosen cartesian direction. Plates with normals perpendicular to this layering direction are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. Additionally the symmetry between the three types of plates is spontaneously broken, as plates with normal along the layering direction have a lower density than the other two types of plates. Intriguingly, the occupied slabs exhibit two-dimensional power-law columnar order even in the presence of a nonzero density of vacancies. In contrast, inter-slab correlations of the two-dimensional columnar order parameter decay exponentially with the separation between the slabs. In the sublattice-ordered phase, there is two-fold ($Z_2$) breaking of lattice translation symmetry along all three cartesian directions. We present numerical evidence that the disordered to layered transition is continuous and consistent with the three-dimensional $O(3)$ universality class, while the layered to sublattice transition is first-order in nature.

cond-mat.stat-mech↗
arXiv2021

Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas

We obtain the phase diagram of fully-packed hard plates on a cubic lattice. Each plate covers an elementary plaquette of the cubic lattice and occupies its four vertices, with each vertex of the cubic lattice occupied by exactly one such plate. We consider the general case with fugacities $s_\mu$ for `$\mu$ plates', whose normal is the $\mu$ direction ($\mu = x,y,z$). At and close to the isotropic point, we find, consistent with previous work, a phase with long-range sublattice order. When two of the fugacities $s_{\rm \mu_1}$ and $s_{\mu_2}$ are comparable, and the third fugacity $s_{\mu_{3}}$ is much smaller, we find a spontaneously-layered phase. In this phase, the system breaks up into disjoint slabs of width two stacked along the $\mu_3$ axis. $\mu_1$ and $\mu_2$ plates are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. In the opposite limit, with $\mu_3 \gg \mu_1 \sim \mu_2$, we find a phase with long-range columnar order, corresponding to simultaneous $Z_2$ symmetry breaking of lattice translation symmetry in directions $\mu_1$ and $\mu_2$. The spontaneously-layered phases display critical behaviour, with power-law decay of correlations in the $\mu_1$ and $\mu_2$ directions when the slabs are stacked in the $\mu_3$ direction, and represent examples of `floating phases' discussed earlier in the context of coupled Luttinger liquids and quasi-two-dimensional classical systems. We ascribe this remarkable behaviour to the constrained motion of defects in this phase, and develop a coarse-grained effective field theoretical understanding of the stability of power-law order in this unusual three-dimensional floating phase.

cond-mat.stat-mech↗
arXiv2021

Bilayer Coulomb phase of two dimensional dimer models: Absence of power-law columnar order

We study the fully-packed dimer model on the bilayer square lattice with fugacity equal to $z$ ($1$) for inter-layer (intra-layer) dimers, and intra-layer interaction $V$ between neighbouring parallel dimers on any elementary plaquette in either layer. For a range of not-too-large $z> 0$ and repulsive interactions $0< V < V_s$ (with $V_s \approx 2.1$), we demonstrate the existence of a {\em bilayer Coulomb phase} with purely dipolar two-point functions, {\em i.e.}, without the power-law columnar order that characterizes the usual Coulomb phase of square and honeycomb lattice dimer models. The transition line $z_{c}(V)$ separating this bilayer Coulomb phase from a large-$z$ disordered phase is argued to be in the inverted Kosterlitz-Thouless universality class. Additionally, we argue for the possibility of a tricritical point at which the bilayer Coulomb phase, the large-$z$ disordered phase and the large-$V$ staggered phase meet in the large-$z$, large-$V$ part of the phase diagram. In contrast, for the attractive case with $ V_{cb} < V \leq 0$ ($V_{cb} \approx -1.2$), we argue that any $z > 0$ destroys the power-law correlations of the $z=0$ decoupled layers, and leads immediately to a short-range correlated state, albeit with a slow crossover for small $|V|$. For $V_{c} < V < V_{cb}$ ($V_{c} \approx -1.55$), we predict that any small nonzero $z$ immediately gives rise to long-range {\em bilayer columnar order} although the $z=0$ decoupled layers remain power-law correlated in this regime; this implies a non-monotonic $z$ dependence of the columnar order parameter for fixed $V$ in this regime. This bilayer columnar ordered state is separated from the large-$z$ disordered state by a line of Ashkin-Teller transitions $z_{\rm AT}(V)$.

cond-mat.stat-mech↗
arXiv2020

Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices

The classic combinatorial construct of {\em maximum matchings} probes the random geometry of regions with local sublattice imbalance in a site-diluted bipartite lattice. We demonstrate that these regions, which host the monomers of any maximum matching of the lattice, control the localization properties of a zero-energy quantum particle hopping on this lattice. The structure theory of Dulmage and Mendelsohn provides us a way of identifying a complete and non-overlapping set of such regions. This motivates our large-scale computational study of the Dulmage-Mendelsohn decomposition of site-diluted bipartite lattices in two and three dimensions. Our computations uncover an interesting universality class of percolation associated with the end-to-end connectivity of such monomer-carrying regions with local sublattice imbalance, which we dub {\em Dulmage-Mendelsohn percolation}. Our results imply the existence of a monomer percolation transition in the classical statistical mechanics of the associated maximally-packed dimer model and the existence of a phase with area-law entanglement entropy of arbitrary many-body eigenstates of the corresponding quantum dimer model. They also have striking implications for the nature of collective zero-energy Majorana fermion excitations of bipartite networks of Majorana modes localized on sites of diluted lattices, for the character of topologically-protected zero-energy wavefunctions of the bipartite random hopping problem on such lattices, and thence for the corresponding quantum percolation problem, and for the nature of low-energy magnetic excitations in bipartite quantum antiferromagnets diluted by a small density of nonmagnetic impurities.

cond-mat.stat-mech↗
arXiv2020

Emergent moments and random singlet physics in a Majorana spin liquid

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility $χ(T)$ of an exactly solvable $S=1/2$ model on the decorated honeycomb lattice with quenched bond disorder and/or vacancies, leading to $χ(T) = {\mathcal C}/T+ {\mathcal D} T^{α(T) - 1}$ where $α(T) \rightarrow 0$ as $T \rightarrow 0$. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder (with different $α(T)$ in the two cases) is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

cond-mat.str-el↗
arXiv2014

Surprise(s) in magnets without net moments

We are all familiar with ferromagnetic and antiferromagnetic materials, in which the localized ionic moments (in case of ionic insulators) or the electronic spins (in case of metals) go into a long-range ordered state with a net macroscopic moment (in case of ferromagnets) or a net macroscopic sublattice magnetization (in case of antiferromagnets). However this behaviour is far from ubiquitous even in ionic insulators with well-developed local moments. Indeed, there are many ionic insulators in which the dominant interactions between the local moments compete with each other, leading to a cooperative paramagnetic state with no ordering of the moments down to the lowest temperatures accessible to experiments. The physics of such magnets without net moments has some interesting and surprising aspects, which are touched upon in this brief review.

cond-mat.str-el↗
arXiv2005

Griffiths phase in the thermal quantum Hall effect

Two dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g. with p_x+ip_y pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, ρ(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'').

cond-mat.mes-hall↗
arXiv2002

A neutron scattering study of two-magnon states in the quantum magnet copper nitrate

We report measurements of the two-magnon states in a dimerized antiferromagnetic chain material, copper nitrate (Cu(NO3)2*2.5D2O). Using inelastic neutron scattering we have measured the one and two magnon excitation spectra in a large single crystal. The data are in excellent agreement with a perturbative expansion of the alternating Heisenberg Hamiltonian from the strongly dimerized limit. The expansion predicts a two-magnon bound state for q ~ (2n+1)pi*d which is consistent with the neutron scattering data.

cond-mat.str-el↗