arXiv subjects

Kedar Damle

Publications and source records attributed to Kedar Damle.

At least 37 records · Page 2Linked to original sources

arXiv2019

Phase diagram of a system of hard cubes on the cubic lattice

We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size $2\times L \times L$ where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size $2\times 2\times L$ where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the $O(3)$ universality class perturbed by cubic anisotropy as predicted by the Landau theory.

cond-mat.stat-mech↗

arXiv2018

Multi-mode superconducting circuits for realizing strongly coupled multi-qubit processor units

Inter-qubit coupling and qubit connectivity in a processor are crucial for achieving high fidelity multi-qubit gates and efficient implementation of quantum algorithms. Typical superconducting processors employ relatively weak transverse inter-qubit coupling which are activated via frequency tuning or microwave drives. Here, we propose a class of multi-mode superconducting circuits which realize multiple transmon qubits with all-to-all longitudinal coupling. These "artificial molecules" directly implement a multi-dimensional Hilbert space that can be easily manipulated due to the always-on longitudinal coupling. We describe the basic technique to analyze such circuits, compute the relevant properties and discuss how to optimize them to create efficient small-scale quantum processors with universal programmability.

quant-ph↗

arXiv2018

Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model

Using a combination of quantum Monte Carlo and exact methods, we study the field-driven saturation transition of the two-dimensional $J$-$Q$ model, in which the antiferromagnetic Heisenberg exchange $(J)$ coupling competes with an additional four-spin interaction $(Q)$ that favors valence-bond solid order. For small values of $Q$, the saturation transition is continuous, and is expected to be governed by zero-scale-factor universality at its upper critical dimension, with a specific form of logarithmic corrections to scaling (first proposed by Sachdev \textit{et al.} [Phys. Rev. B \textbf{50}, 258 (1994)]). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev \textit{et al.} We also show that the saturation transition becomes first order above a critical coupling ratio $(Q/J)_{\rm min}$ and is accompanied by magnetization jumps---metamagnetism. We obtain an exact solution for $(Q/J)_{\rm min}$ using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2017

Semiclassical theory for liquid-like behaviour of the frustrated magnet $\mathrm{Ca}_{10}\mathrm{Cr}_{7}\mathrm{O}_{28}$

We identify the low energy effective Hamiltonian that is expected to describe the low temperature properties of the frustrated magnet $\mathrm{Ca}_{10}\mathrm{Cr}_{7}\mathrm{O}_{28}$. Motivated by the fact that this effective Hamiltonian has $S=3/2$ effective moments as its degrees of freedom, we use semiclassical spinwave theory to study the $T=0$ physics of this effective model and argue that singular spinwave fluctuations destabilize the spiral order favoured by the exchange couplings of this effective Hamiltonian. We also use a combination of classical Monte-Carlo simulations and molecular dynamics, as well as analytical approximations, to study the physics at low, nonzero temperatures. The results of these nonzero temperature calculations capture the liquid-like structure factors observed in the temperature range accessed by recent experiments. Additionally, at still lower temperatures, they predict that a transition to nematic order in the bond energies reflects itself in the spin channel in the form of a crossover to a regime with large but finite correlation length for spiral spin correlations and a corresponding slowing down of spin dynamics.

cond-mat.str-el↗

arXiv2017

Field-driven quantum phase transitions in $S=1/2$ spin chains

We study the magnetization process of a 1D extended Heisenberg model, the $J$-$Q$ model, as a function of an external magnetic field. In this model, $J$ represents the traditional antiferromagnetic Heisenberg exchange and $Q$ is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value $q_c\approx 0.85$ where $q\equiv Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for $q>q_{\rm min}$, where we have calculated $q_{\rm min}=2/9$ exactly. For $q>q_{\rm min}$ two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for $q>q_{\rm min}$. Our results show that neither geometric frustration nor spin-anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated $J_1$-$J_2$ chain ($J_1>0$, $J_2<0$), but only if $J_2$ is spin-anisotropic. We also investigate quantum-critical scaling near the transition into the fully polarized state for $q\le q_{\rm min}$ at $T>0$. While the expected `zero-scale-factor' universality is clearly seen for $q=0$ and $q\ll q_{\rm min}$; closer to $q_{\rm min}$ we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at $q_{\rm min}$, which leads to a cross-over at a temperature $T^*(q)$ between logarithmic tricritical scaling and zero-scale-factor universality, with $T^*(q)\to 0$ when $q\to q_{\rm min}$.

cond-mat.str-el↗

arXiv2016

Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions

We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbours on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbour couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wavevector.

cond-mat.stat-mech↗

arXiv2016

Implementation of pairwise longitudinal coupling in a three-qubit superconducting circuit

We present the "trimon", a multi-mode superconducting circuit implementing three qubits with all-to-all longitudinal coupling. This always-on interaction enables simple implementation of generalized controlled-NOT gates which form a universal set. Further, two of the three qubits are protected against Purcell decay while retaining measurability. We demonstrate high-fidelity state swapping operations between two qubits and characterize the coupling of all three qubits to a neighbouring transmon qubit. Our results offer a new paradigm for multi-qubit architecture with applications in quantum error correction, quantum simulations and quantum annealing.

quant-ph↗

arXiv2016

Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets

We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates in a sign-problem-free way a broad class of frustrated $S=1/2$ models with competing antiferromagnetic interactions. Our scheme uses the basis of total spin eigenstates of clusters of spins to avoid the severe sign problem faced by other QMC methods. We also flag important limitations of the new method, and comment on possibilities for further progress.

cond-mat.str-el↗

arXiv2016

Vacancy-induced low-energy states in undoped graphene

We demonstrate that a nonzero concentration $n_v$ of static, randomly-placed vacancies in graphene leads to a density $w$ of zero-energy quasiparticle states at the band-center $ε=0$ within a tight-binding description with nearest-neighbour hopping $t$ on the honeycomb lattice. We show that $w$ remains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder, and depends sensitively on $n_v$ and correlations between vacancy positions. For low, {\em but not-too-low} $|ε|/t$ in this compensated case, we show that the density of states (DOS) $ρ(ε)$ exhibits a strong divergence of the form $ρ_{\rm 1D}(ε) \sim |ε|^{-1}/ [\log(t/|ε|)]^{(y+1)} $, which crosses over to the universal low-energy asymptotic form expected on symmetry grounds $ρ_{\rm GW}(ε) \sim |ε|^{-1}e^{-b[\log(t/|ε|)]^{2/3} }$ below a crossover scale $ε_c \ll t$. $ε_c$ is found to decrease rapidly with decreasing $n_v$, while $y$ decreases much more slowly.

cond-mat.str-el↗

arXiv2016

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

A transverse magnetic field $Γ$ is known to induce antiferromagnetic three-sublattice order of the Ising spins $σ^z$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wavevector ${\bf Q}$: $\langle σ^z(\vec{R}) σ^z(0)\rangle \sim \cos({\mathbf Q}\cdot \vec{R}) /|\vec{R}|^{η(T)}$ with the temperature-dependent power-law exponent $η(T) \in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility $χ_{u}(L)$ of an $L \times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence $χ_{u}(L)\sim L^{2- 9 η}$ when $η(T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility $χ_{u}(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, $χ_{u}(B) \sim |B|^{-\frac{4 - 18 η}{4-9η}}$ for $η(T) \in (1/9, 2/9)$, although there is no ferromagnetic long-range order in the low temperature state.

cond-mat.stat-mech↗

arXiv2015

Two-step melting of three-sublattice order in $S=1$ easy-axis triangular lattice antiferromagnets

We consider $S=1$ triangular lattice Heisenberg antiferromagnets with a strong single-ion anisotropy $D$ that dominates over the nearest-neighbour antiferromagnetic exchange $J$. In this limit of small $J/D$, we study low temperature ($T \sim J \ll D$) properties of such magnets by employing a low-energy description in terms of hard-core bosons with nearest neighbour repulsion $V \approx 4J + J^2/D$ and nearest neighbour unfrustrated hopping $t \approx J^2/2D$. Using a cluster Stochastic Series Expansion (SSE) algorithm to perform sign-problem-free quantum Monte Carlo (QMC) simulations of this effective model, we establish that the ground-state three-sublattice order of the easy-axis spin-density $S^z(\vec{r})$ melts in zero field ($B=0$) in a {\em two-step} manner via an intermediate temperature phase characterized by power-law three-sublattice order with a temperature dependent exponent $η(T) \in [\frac{1}{9}, \frac{1}{4}]$. For $η(T) < \frac{2}{9}$ in this phase, we find that the uniform easy-axis susceptibility of an $L \times L$ sample diverges as $χ_L \sim L^{2-9 η}$ at $B=0$, consistent with a recent prediction that the thermodynamic susceptibility to a uniform field $B$ along the easy axis diverges at small $B$ as $χ_{\rm easy-axis}(B) \sim B^{-\frac{4-18η}{4-9η}}$ in this regime.

cond-mat.str-el↗

arXiv2015

Quantum cluster algorithm for frustrated Ising models in a transverse field

Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this new algorithm, we show that a relatively small, ferromagnetic next-nearest neighbour coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic three-sublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.

cond-mat.str-el↗

arXiv2015

Classical spin-liquid on the maximally frustrated honeycomb lattice

We show that the honeycomb Heisenberg antiferromagnet with $J_1/2=J_2=J_3$, where $J_{1/2/3}$ are first-, second- and third-neighbour couplings respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with non-magnetic ions, fractionalised degrees of freedom carrying $1/3$ of the free moment emerge. Their effective description in the limit of low-temperature is that of spins randomly located on a triangular lattice, with a frustrated interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder, which comes with a clear experimental diagnostic.

cond-mat.str-el↗

arXiv2015

Melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices

When the constituent spins have an energetic preference to lie along an easy-axis, triangular and Kagome lattice antiferromagnets often develop long-range order that distinguishes the three sublattices of the underlying triangular Bravais lattice. In zero magnetic field, this three-sublattice order melts {\em either} in a two-step manner, {\em i.e.} via an intermediate phase with power-law three-sublattice order controlled by a temperature dependent exponent $η(T) \in (\frac{1}{9},\frac{1}{4})$, {\em or} via a transition in the three-state Potts universality class. Here, I predict that the uniform susceptibility to a small easy-axis field $B$ diverges as $χ(B) \sim |B|^{-\frac{4 - 18 η}{4-9η}}$ in a large part of the intermediate power-law ordered phase (corresponding to $η(T) \in (\frac{1}{9},\frac{2}{9})$), providing an easy-to-measure thermodynamic signature of two-step melting. I also show that these two melting scenarios can be generically connected via an intervening multicritical point, and obtain numerical estimates of multicritical exponents.

cond-mat.stat-mech↗

arXiv2015

Resonating valence-bond physics on the honeycomb lattice

We study bond and spin correlations of the nearest-neighbour resonating valence bond (RVB) wavefunction for a SU($2$) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wavefunction are short-ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\vec{r}) \sim \cos({\mathbf Q}\cdot {\vec{r}}) /|{\vec{r}}|^{η_w(2)}$, where ${\mathbf Q} = (2π/3, -2π/3)$ is the wavevector corresponding to "columnar" valence-bond solid order on the honeycomb lattice, and $η_w(2) \approx 1.49(3)$. We use a recently introduced large-$g$ expansion approach to relate bond-energy correlators of the SU($g$) wavefunction to dimer correlations of an interacting fully-packed dimer model with a three-dimer interaction of strength $V(g)=-\log(1+1/g^2)$. Putting $g=2$, we find numerically that the dimer correlation function $D^{d}(\vec{r})$ of this dimer model has power-law behaviour $D^{d}(\vec{r}) \sim \cos({\mathbf Q}\cdot {\vec{r}}) /|{\vec{r}}|^{η_d(2)}$ with $η_d(2) \approx 1.520(15)$, in rather good agreement with the wavefunction results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the SU($g$) wavefunction are consistently well-reproduced by the corresponding dimer correlations in the interacting dimer model.

cond-mat.str-el↗

arXiv2015

Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers

We show that critical exponents of the transition to columnar order in a {\em mixture} of $2 \times 1$ dimers and $2 \times 2$ hard-squares on the square lattice {\em depends on the composition of the mixture} in exactly the manner predicted by the theory of Ashkin-Teller criticality, including in the hard-square limit. This result settles the question regarding the nature of the transition in the hard-square lattice gas. It also provides the first example of a polydisperse system whose critical properties depend on composition. Our ideas also lead to some interesting predictions for a class of frustrated quantum magnets that exhibit columnar ordering of the bond-energies at low temperature.

cond-mat.stat-mech↗

arXiv2015

Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, {\em i.e.} $J(r)\sim -A\ln r$ in $d=2$ and $J(r)\sim A/r$ in $d=3$. This arises naturally as the $T\rightarrow 0$ limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of $A$ in both $d=2$ and $d=3$. In $d=2$, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, $A=\infty$, while no such transition seems to exist at all in $d=3$. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem.

cond-mat.str-el↗

arXiv2015

Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet

We use Quantum Monte-Carlo methods to study the ground state phase diagram of a S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange J (favoring Néel order) competes with two different multi-spin interaction terms: a six-spin interaction Q_3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction Q_2 that favors staggered VBS order. For Q_3 ~ Q_2 >> J, we establish that the competition between the two different VBS orders stabilizes Néel order in a large swathe of the phase diagram even when J is the smallest energy-scale in the Hamiltonian. When Q_3 >> (Q_2,J) (Q_2 >> (Q_3,J)), this model exhibits at zero temperature phase transition from the Néel state to a columnar (staggered) VBS state. We establish that the Néel-columnar VBS transition is continuous for all values of Q_2, and that critical properties along the entire phase boundary are well-characterized by critical exponents and amplitudes of the non-compact CP^1 (NCCP^1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising three-fold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the Q_2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional XY model with a four-fold anisotropy field which is known to be weakly irrelevant at the three-dimensional XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations.

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