Two-dimensional Spin Systems Research Articles

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems**Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171397), the National Natural Science Foundation of China (Grant Nos. 11535004, 11375086, 1175085, and 11120101005), the Foundation for Encouragement of College of Sciences (Grant No. LYLZJJ1616), and the Pre-research Foundation of Army Engineering University

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence (SC) and square of quantum discord (SQD). The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Building crystalline topological phases from lower-dimensional states

We study the classification of symmetry protected topological (SPT) phases with crystalline symmetry (cSPT phases). Focusing on bosonic cSPT phases in two and three dimensions, we introduce a simple family of cSPT states, where the system is comprised of decoupled lower-dimensional building blocks that are themselves SPT states. We introduce a procedure to classify these block states, which surprisingly reproduces a classification of cSPT phases recently obtained by Thorngren and Else using very different methods, for all wallpaper and space groups. The explicit constructions underlying our results clarify the physical properties of the phases classified by Thorngren and Else, and expose additional structure in the classification. Moreover, the states we classify can be completely characterized by point group SPT (pgSPT) invariants and related weak pgSPT invariants that we introduce. In many cases, the weak invariants can be visualized in terms of translation-symmetric stacking of lower-dimensional pgSPT states. We apply our classification to propose a Lieb-Shultz-Mattis type constraint for two-dimensional spin systems with only crystalline symmetry, and establish this constraint by a dimensional reduction argument. Finally, the surprising matching with the Thorngren-Else classification leads us to conjecture that all SPT phases protected only by crystalline symmetry can be built from lower-dimensional blocks of invertible topological states. We argue that this conjecture holds if we make a certain physically reasonable but unproven assumption.

Effective description of correlations for states obtained from conformal field theory

We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains and they are similar to lattice Laughlin states in two dimensions. We show that their zz correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory that explains the behavior of the correlations: a polynomial decay in one dimension and at the edge of a two-dimensional system and an exponential decay in the bulk of a two-dimensional system. We test the validity of our approximation by comparing it to Monte Carlo computations.

Surface energies emerging in a microscopic, two-dimensional two-well problem

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.

Dynamically enriched topological orders in driven two-dimensional systems

Time-periodic driving enables new nonequilibrium quantum phases of matter with topologically protected and quantum coherent motion that would be forbidden in thermal equilibrium. This work uncovers two new classes of driven topological phases in driven two-dimensional spin systems: i) Floquet symmetry protected topological phases, which are driven and interacting analogs of topological insulators whose edge states are protected against disorder and localization; and ii) Floquet enriched topological orders, in which time-dependent driving ``breaks'' the spins into anyonic particles with fractional statistics and oscillating topological charge. The physics of these phases is explored by constructing toy models that can be explicitly solved despite the presence of strong interactions.

Robust quantum state transfer via topologically protected edge channels in dipolar arrays

We show how to realise quantum state transfer between distant qubits using the chiral edge states of a two-dimensional topological spin system. Our implementation based on Rydberg atoms allows to realise the quantum state transfer protocol in state-of-the-art experimental setups. In particular, we show how to adapt the standard state transfer protocol to make it robust against dispersive and disorder effects.

Post-annealing effects in two-dimensional spin system SrCuO<sub>2</sub> sputtered on glass substrate

Post-annealing effects in two-dimensional spin system SrCuO<sub>2</sub> sputtered on glass substrate

Effect of the phase transition to the ferroquadrupolar phase on spin transport in the biquadratic antiferromagnet of the triangular lattice

We use the SU(N) Schwinger boson formalism to study the spin transport in the S=1 biquadratic frustrated Heisenberg antiferromagnetic model in the triangular lattice, considering the next-nearest-neighbors interactions J2. We have obtained a jump in the spin conductivity in the point of cusp of the phase diagram −η vs. −α of the model at T=0, which represents the force of the biquadratic coupling versus the next-nearest-neighbor coupling (K vs. J2). We have obtained also a superfluid behavior for the spin transport in the DC limit for this system similar to ones recently obtained for other two-dimensional frustrated spin systems. We consider all the couplings, first and second couplings as antiferromagnetic.

Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point

We study the level structure of excitations at the "deconfined" critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J$-$Q$ model as an example. Energy gaps in different spin ($S$) and momentum (${\bf k}$) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at ${\bf k}=(0,0)$, $(\pi,0)$, $(0,\pi)$, and $(\pi,\pi)$, as inferred from two-spinon excitations ($S=0$ and $S=1$ states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).

A bilayer Double Semion model with symmetry-enriched topological order

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topological Order with a global spin–flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trivial braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.

Neutron spin-echo study of the critical dynamics of spin-52antiferromagnets in two and three dimensions

We report a neutron spin-echo study of the critical dynamics in the $S=5/2$ antiferromagnets MnF$_2$ and Rb$_2$MnF$_4$ with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the N\'eel temperature, $T_N$. By taking advantage of the $\mu\text{eV}$ energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents $z$ for both longitudinal and transverse fluctuations. In MnF$_2$, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents $z$ in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the critical dynamics crosses over from the expected 2D Heisenberg behavior for $T\gg T_N$ to a scaling regime with exponent $z = 1.387(4)$, which has not been predicted by theory and may indicate the influence of long-range dipolar interactions.

Implementing the density matrix embedding theory with the hierarchical mean-field approach

We show an implementation of density matrix embedding theory (DMET) for the spin lattice of infinite size. It is indeed a special form of hierarchical mean-field (HMF) theory. In the method, we divide the lattice into a small part and a large part. View the small part as an impurity, embedding in the large part, which is viewed as the environment. We deal the impurity with a high accuracy method. But treat the environment with a low-level method: the states of the environment nearby the impurity are expressed by a set of multiple block product states, while the distant parts are treated by mean-field consideration. Our method allows for the computation of the ground state of the infinite two-dimensional quantum spin systems. In the text, we take the frustrated Heisenberg model as an example to test our method. The ground state energy we calculated can reach a high accuracy. We also calculate the magnetization, and the fidelity to study the quantum phase transitions.

Direct visualization of surface phase of oxygen molecules physisorbed on Ag(111) surface: A two-dimensional quantum spin system

We report on the real-space observation of the two-dimensional distorted triangular lattice of physisorbed oxygen $({\mathrm{O}}_{2})$ molecules on an Ag(111) surface by low-temperature scanning tunneling microscopy. The physisorbed state of the ${\mathrm{O}}_{2}$ monolayers was confirmed by measuring their thermal stability, which showed good agreement with previous thermal desorption spectroscopy. The distortion of the observed lattice was reproduced quantitatively by considering the intermolecular exchange interaction in Monte Carlo calculations, indicating a critical role of antiferromagnetic ordering of ${\mathrm{O}}_{2}$ spins. In tunneling spectra, the Kondo resonance was not observed on the ${\mathrm{O}}_{2}$ layer at 4.7 K unlike the case of physisorbed ${\mathrm{O}}_{2}$ on Ag(110). These results indicate that an intrinsic $S=1$ spin of the ${\mathrm{O}}_{2}$ molecules was preserved to form a two-dimensional antiferromagnetic quantum spin system on the surface.

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyse the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the low-energy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally-damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.

Chiral spin liquids in arrays of spin chains

We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.

Superconducting Phase in λ-(BEDT-STF)2GaCl4 at High Pressures

Electrical resistivity measurements under pressure were conducted on the organic conductor λ-(BEDT-STF)2GaCl4, which is situated between λ-(ET)2GaCl4 and λ-(BETS)2GaCl4. Magnetic susceptibility was also measured at ambient pressure. A drop in resistivity, which is associated with the superconducting transition, was observed at Tc ≈ 5 K above 1.22 GPa. The superconducting phase was confirmed by pair-breaking under a magnetic field. This is the first observation of superconductivity in λ-(BEDT-STF)2GaCl4. The temperature dependence of spin susceptibility suggests a two-dimensional antiferromagnetic spin system without any magnetic ordering. The phase adjacent to the superconducting phase in λ-type systems is not the antiferromagnetic phase, unlike the case for κ-(ET)2X.

Anomalous response in the vicinity of spontaneous symmetry breaking

We propose a mechanism to induce negative AC permittivity in the vicinity of a ferroelectric phase transition involved with spontaneous symmetry breaking. This mechanism makes use of responses at low frequency, yielding a high gain and a large phase delay, when the system jumps over the free-energy barrier with the aid of external fields. We illustrate the mechanism by analytically studying spin models with the Glauber-typed dynamics under periodic perturbations. Then, we show that the scenario is supported by numerical simulations of mean-field as well as two-dimensional spin systems.

Magnons and excitation continuum in XXZ triangular antiferromagnetic model: Application toBa3CoSb2O9

We investigate the excitation spectrum of the triangular-lattice antiferromagnetic $XXZ$ model using series expansions and mean field Schwinger bosons approaches. The single-magnon spectrum computed with series expansions exhibits rotonic minima at the middle points of the edges of the Brillouin zone, for all values of the anisotropy parameter in the range $0\leq J^z/J\leq1$. Based on the good agreement with series expansions for the single-magnon spectrum, we compute the full dynamical magnetic structure factor within the mean field Schwinger boson approach to investigate the relevance of the $XXZ$ model for the description of the unusual spectrum found recently in $Ba_3CoSb_2O_9$. In particular, we obtain an extended continuum above the spin wave excitations, which is further enhanced and brought closer to those observed in $Ba_3CoSb_2O_9$ with the addition of a second neighbor exchange interaction approximately 15% of the nearest-neighbor value. Our results support the idea that excitation continuum with substantial spectral-weight are generically present in two-dimensional frustrated spin systems and fractionalization in terms of {\it bosonic} spinons presents an efficient way to describe them.

Emergent topological excitations in a two-dimensional quantum spin system

We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo simulations in the valence bond basis. A topological excitation with winding number $|W|>0$ contains domain walls, which are unstable due to the emergence of long valence bonds in the wave function, unlike in effective descriptions with the quantum dimer model. We find that the life time of the winding number in imaginary time diverges as a power of the system length $L$. The energy can be computed within this time (i.e., it converges toward a "quasi-eigenvalue" before the winding number decays) and agrees for large $L$ with the domain-wall energy computed in an open lattice with boundary modifications enforcing a domain wall. Constructing a simplified two-state model and using the imaginary-time behavior from the simulations as input, we find that the real-time decay rate out of the initial winding sector is exponentially small in $L$. Thus, the winding number rapidly becomes a well-defined conserved quantum number for large systems, supporting the conclusions reached by computing the energy quasi-eigenvalues. Including Heisenberg exchange interactions which brings the system to a quantum-critical point separating the valence-bond solid from an antiferromagnetic ground state (the putative "deconfined" quantum-critical point), we can also converge the domain wall energy here and find that it decays as a power-law of the system size. Thus, the winding number is an emergent quantum number also at the critical point, with all winding number sectors becoming degenerate in the thermodynamic limit. This supports the description of the critical point in terms of a U(1) gauge-field theory.