Nearest-neighbor Interactions Research Articles

Influence of errors on the transport of quantum information through distant quantum dot spin qubits

The ability to connect distant qubits plays a role in quantum computing and systems candidates for quantum computation must be able to interact their constituent qubits. We model the quantum dot spin qubits by a spin chain with nearest-neighbors interaction. Within this model, we interact distant qubits by consecutive SWAP gates. The SWAP gate exchanges the information of two different qubits and it is obtained by a time-dependent pulse. Also, we implement the CNOT gate, which is fundamental to universal quantum computation. These gates are applied in a system free from decoherence, which provides a fidelity with high accuracy. Furthermore, we analyze the situation where dephasing, amplitude-damping, and depolarizing types of errors occur in each site of the chain. We found that the order of the SWAP and CNOT gates is important and it can lead to a relevant difference in fidelity when the number of qubits is large.

Electronic circular dichroism of proteins computed using a diabatisation scheme

ABSTRACT Circular dichroism (CD) spectroscopy is a powerful technique employed to study the structure of biomolecules. More accurate calculation of CD from first principles will aid both computational and experimental studies of protein structure and dynamics. We apply a diabatisation scheme to improve the description of nearest neighbour interactions between two electronic transitions (nπ* and πnbπ*) localised on each individual peptide bond (amide group) in a protein. These interactions are incorporated into DichroCalc, an exciton-based computational method to calculate CD, and yield improvements over the standard DichroCalc parameter set, particularly for calculation of CD for important secondary structural elements such as an α helix.

Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbors interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a 'spin-locked' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a 'polarized holonic' phase, and a crystalline phase at the filling 2/5, that we address via semi-classical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.

Thermodynamics of the metal-insulator transition in the extended Hubbard model from determinantal quantum Monte Carlo

Using finite-temperature determinantal quantum Monte Carlo simulations, we examine the thermodynamic properties of the extended Hubbard model on the half-filled square lattice in the Slater regime at intermediate coupling. We consider both the case of nearest-neighbor interactions and long-range Coulomb interactions, for coupling strengths in which the presence of non-local interactions still allows us to perform sign-problem free quantum Monte Carlo simulations. In particular, we assess a recently proposed scenario from variational calculations in terms of a first-order metal-insulator transition in this interaction regime.

Understanding the propagation of excitations in quantum spin chains with different kind of interactions

The dynamical behavior of the quantum state of different quantum spin chains, with designed site-dependent interaction strengths, is analyzed when the initial state belongs to the one excitation subspace. Our results show that the inhomogeneous chains transfer single excitations with near-perfect fidelity for two different spin chain Hamiltonians. The first one is the ferromagnetic Heisenberg Hamiltonian with nearest neighbor interactions. The second spin chain has long-range anisotropic interactions, ferromagnetic in one direction and antiferromagnetic in the orthogonal plane. Both designed chains have in common a partially ordered spectrum and well-localized eigenvectors. This physical trait unifies the description of both kinds of systems.

Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

Shaken Dynamics: An Easy Way to Parallel Markov Chain Monte Carlo

We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function H(sigma ). These dynamics turn out to be reversible and their stationary measure is explicitly determined. Convergence to equilibrium and relation of the stationary measure to the usual Gibbs measure are discussed when the dynamics is defined on mathbb {Z}^2. Further it is shown how these dynamics can be used to define natively parallel algorithms to face problems in the context of combinatorial optimization.

Galton–Watson Trees with First Ancestor Interaction

We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given node of the maximal tree is equal to the number of offspring if the node is present in the random tree and equal to -1 otherwise. We introduce nearest neighbour interactions favouring pairs of neighbours which both have a relatively large offspring. We then prove (1) correlation inequalities and (2) recursion relations for generating functions, mean number of external nodes, interaction energy and the corresponding variances. The resulting quadratic dynamical system, in two dimensions or more depending on the desired number of moments, yields almost exact numerical results. The balance between offspring distribution and coupling constant leads to a phase diagram for the analogue of the extinction probability. On the transition line the mean number of external nodes in generation $n+1$ is found numerically to scale as $n^{-2}$.

Residual entropy of ice Ih by Wang–Landau Monte Carlo simulation of an effective Ising model

Accurate evaluation of the residual entropy of three-dimensional ice systems remains a difficult task. In this work, we estimate the residual entropy of ice Ih (ordinary ice) by an improvement of the Wang–Landau Monte Carlo algorithm, which directly calculates the density of states of the system. We define an effective three-dimensional Ising model with nearest-neighbour interactions, and introduce the mapping of the spin configurations of this Ising model into the hydrogen configurations of ice Ih. The ground states of this Ising model are equivalent with the hydrogen configurations obeying the ice rules, therefore the ground state degeneracy directly determines the residual entropy. Our estimate is in good agreement with the famous theoretical approximation by Nagle in 1966, and other results evaluated from various methods. The advantage of making use of the equivalent Ising model is discussed. It is convenient to extend our approach to other lattice systems.

Signatures of spin-liquid state in a 3D frustrated lattice compound KSrFe2(PO4)3 with S = 5/2

A quantum spin-liquid is a spin disordered state of matter in which spins are strongly correlated and highly entangled with low-energy excitations. It has been often found in two-dimensional S = ½, highly frustrated spin networks but rarely observed in three-dimensional (3D) frustrated quantum magnets. Here, KSrFe2(PO4)3, forming a complicated 3D frustrated lattice with a spin moment S = 5/2, is investigated by thermodynamic, neutron diffraction measurements and electronic structure calculations. Despite the relatively sizable Curie–Weiss temperature θCW = −70 K, a conventional magnetic long-range order is confirmed to be absent down to 0.19 K. The magnetic heat capacity data follow the power-law behavior at the lowest temperature region, supporting gapless excitations in a 3D spin-liquid state. Strong geometrical spin frustration responsible for the spin-liquid feature is understood as originating from the almost comparable five competing nearest-neighbor antiferromagnetic exchange interactions, which form the complicated 3D frustrated spin network. All these results suggest that the compound KSrFe2(PO4)3, representing a unique 3D spin frustrated network, could be a rare example of forming a gapless spin-liquid state even with a large spin moment of S = 5/2.

Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials

A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moir\'e structures of transition metal dichalcogenides can be used to simulate extended versions that include non-local density-density interactions. We study competing instabilities of interacting electrons in such an extended Hubbard model on the triangular lattice near a filling where the density of states has a Van Hove singularity. We employ a truncated-unity functional renormalization group approach to investigate two cases: a paradigmatic minimally extended Hubbard model and a specific model with parameters that are applicable to hetero-bilayers of transition metal dichalcogenides. We unravel rich phase diagrams, including tendencies to spin-density-wave order and unconventional pairing, which can give rise to topological superconductivity. We classify the symmetry of the superconducting instabilities according to their irreducible representations and show that higher lattice harmonics are dominant when the nearest-neighbor interaction is sizable indicating pair formation between second-nearest neighbors. The phenomenological consequences can be enhanced spin and thermal quantum Hall responses in a topological superconductor.

Subdiffusive energy transport and antipersistent correlations due to the scattering of phonons and discrete breathers

While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that, in the range of system size investigated, the energy subdiffusion can take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. In particular, we show that the interaction range dependence of antipersistent energy-current correlations are relevant to this special type of energy subdiffusion. The underlying mechanisms are related to the various scattering processes of phonons and discrete breathers. Our results shed light on understanding the extremely slow energy transport.

Fractional vortices, Z2 gauge theory, and the confinement-deconfinement transition

In this Letter we discuss the classical three-dimensional XY model whose nearest-neighbor interaction is a mixture of $cos({\ensuremath{\theta}}_{i}\ensuremath{-}{\ensuremath{\theta}}_{j})$ (ferromagnetic) and $cos2({\ensuremath{\theta}}_{i}\ensuremath{-}{\ensuremath{\theta}}_{j})$ (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a noncompact $U(1)$ gauge field, the half-integer vortices interact with an extra interaction mediated by a ${\mathbb{Z}}_{2}$ gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the `t Hooft loops, and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.

Long-distance entanglement in antiferromagnetic XXZ spin chain with alternating interactions

In this paper, the quantum entanglement (concurrence) of one-dimensional antiferromagnetic XXZ spin system with alternating nearest-neighbor interactions is studied by means of the density matrix renormalization group method with matrix product state form. The ground-state energy, long-distance entanglement and entanglement distribution are calculated, and the effects of alternating interactions, anisotropy and open boundary condition on them are discussed. It is found that the alternating interactions favor the generation and development of long-distance entanglement, while anisotropy inhibits that. For the entanglement distribution of the system, it is also found that the alternating interactions and open boundary condition induce the dimerization on odd and even bonds, respectively, while anisotropy always suppresses this behavior. Furthermore, both nearest-neighbor and long-distance entanglements are converged to certain values with increasing system size.

Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields

We investigate the dynamic structure factor of the antiferromagnetic Kitaev honeycomb model in a magnetic field by applying perturbative continuous unitary transformations about the high-field limit. One- and two-quasiparticle properties of the dressed elementary spin-flip excitations of the high-field polarized phase are calculated which account for most of the spectral weight in the dynamic structure factor. We discuss the evolution of spectral features in these quasiparticle sectors in terms of one-quasiparticle dispersions, two-quasiparticle continua, the formation of antibound states, and quasiparticle decay. In particular, a comparably strong spectral feature above the upper edge of the upmost two-quasiparticle continuum represents three antibound states which form due to nearest-neighbor density-density interactions.

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbour nonreciprocal hopping, in the presence of repulsive nearest-neighbour interactions. At half filling, we find two $\mathcal{PT}$ transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.

Localization phenomena in a one-dimensional phononic lattice with finite mass modulation: Beyond nearest-neighbor interaction

One-dimensional phononic systems beyond conventional nearest-neighbor interaction have not been well explored, to the best of our knowledge. In this work, we critically investigate the localization properties of a 1D phononic lattice in presence of second-neighbor interaction along with the nearest-neighbor one. A finite modulation in masses is incorporated following the well known Aubry-Andre-Harper (AAH) form to make the system a correlated disordered one. Solving the motion equations we determine the phonon frequency spectrum, and characterize the localization properties of the individual phononic states by calculating inverse participation ratio (IPR). The key aspect of our analysis is that, in the presence of second-neighbor interaction, the phonon eigenstates exhibit frequency dependent transition from sliding to the pinned phase upon the variation of the modulation strength, exhibiting a mobility edge. This is completely in contrast to the nearest-neighbor interaction case, where all the states get localized beyond a particular modulation strength, and thus, no mobility edge appears. Our analysis can be utilized in many aspects to regulate phonon transmission through similar kind of aperiodic lattices that are described beyond the usual nearest-neighbor interaction.

Random translation-invariant Hamiltonians and their spectral gaps

We consider random translation-invariant frustration-free quantum spin Hamiltonians on ZD in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result is that, under a small rank constraint, the Hamiltonians are automatically frustration-free and they are gapped with a positive probability. This extends previous results on 1D spin chains to all dimensions. The argument additionally controls the local gap. As an application, we obtain a 2D area law for a cut-dependent ground state via recent AGSP methods of Anshu-Arad-Gosset.

Functional renormalization of spinless triangular-lattice fermions: N-patch vs. truncated-unity scheme

We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability occurs at Van Hove filling and f-wave and p-wave pairing emerge when the filling is reduced. In the repulsive case, we obtain a charge density wave at Van Hove filling and extended p-wave pairing with reduced filling. The p-wave pairing solution is doubly degenerate and can realize chiral p+ip superconductivity with different Chern numbers in the ground state. We discuss implications for strongly correlated spin-orbit coupled hexagonal electron systems such as moiré heterostructures.Graphic

Supercooled Jahn-Teller ice

When the spins on the frustrated pyrochlore lattice obey the celebrated 2-$in$-2-$out$ ice rule, they stay in a correlated disordered phase and break the third law of thermodynamics. Similarly, if the atomic ions on the pyrochlore lattice move in and outward of the tetrahedra, they may obey a constraint resembling the ice rule. We discover that a model for pyrochlore molybdates $A_2$Mo$_2$O$_7$ ($A=$Y, Dy, Tb) exhibits a "supercooled ice" state of the displacement degrees of freedom of Mo$^{4+}$ ions, when we take account of the Jahn-Teller (JT) effect. The JT effect occurs when the lattice distortions reduce the symmetry of the local crystal field, resulting in the orbital-energy-splitting that causes the local energy gain. Unlike the standard JT effect that leads to periodic long range ordering, the displacements of Mo$^{4+}$ ions are disordered following the ice-like rule. We microscopically derive a model that describes this situation by having the 2nd and 3rd neighbor interactions between in-out lattice displacements comparably as strong as the nearest neighbor interactions of standard ice. There, the well-known nearly flat energy landscape of the ice state is altered to a metastable highly quasi-degenerate ice-like liquid state coexisting with a crystalline-like ground state. Our Monte Carlo simulations show that this liquid remains remarkably stable down to low temperatures by avoiding the putative first order transition. The relaxation in the supercooled JT ice state exhibits glassy dynamics with a plateau structure. They fit the feature of a "good glassformer" very often found in molecular liquids, but that has never been observed in material solids. The high glass-forming ability of the interacting lattice degrees of freedom will play a key role in the spin-glass transition of the material.