Session W22: Magnetic Phase Transitions II

Bound states and E8 symmetry effects in perturbed quantum Ising chains

In a recent experiment on $\mathrm{CoNb}_2\mathrm{O}_6$, Coldea et al. found for the first time experimental evidence of the exceptional Lie algebra $E_8$. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of $\mathrm{CoNb}_2\mathrm{O}_6$ incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. We compare the signatures of this model to those found in the transverse Ising chain in a longitudinal field and to experimental data, with focus on how far the effects of integrability extends and how robust they are to the additional interactions. The excitation spectra show bound states characteristic of the weakly broken $E_8$ symmetry and a bound state continuum carrying spectral weight comparable to the higher bound states.   

Comparison between two simple models for the magnetoelectric interaction in multiferroics

We developed numerical calculations to simulate the magnetoelectric coupling in multiferroic compounds, using the Monte Carlo technique. Two simple models were used to simulate the compounds. In the first one, the magnetic ions are represented by a spin 1/2 2D\ Ising lattice of ions, and the electric lattice by classical moments, coupled one to one with the magnetic moments. The coupling between both lattices allows to the leading lattice, that is, the magnetic one, to change the orientation of the electrical dipoles in one direction perpendicular to the magnetic dipoles. This direction was chosen to accomplish the symmetry requirements of the magnetoelectric effect. In the second case, the magnetic lattice is also a 2D Ising lattice, but the electric momenta are in a lattice that also behaves as an Ising lattice, perpendicular to the magnetic moments. In this case, the one-to-one coupling of the electric and magnetic momenta is represented by a two-valued energy parameter, allowing the possibility of independent transition temperatures for both lattices. Both models contain three independent parameters. We studied the physical properties obtained with both models, as functions of the ratio of the three parameters. The results in both cases allowed us to compare changes in the physics of the models, and with the physics of compounds measured experimentally.   

The itinerant ferromagnetic phase of the Hubbard model

Using a newly developed quantum Monte Carlo technique, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-U Hubbard model. By decreasing the electron density, a discontinuous transition to a paramagnetic phase is observed, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition. The remarkable stability of itinerant ferromagnetism renews the hope to describe this phenomenon within a purely kinetic mechanism and will facilitate the validation of experimental quantum simulators with cold atoms loaded in optical lattices.   

Two species Bosonic Hubbard model in a two-dimensional optical lattice

We study a two-component hardcore bosonic Hubbard model in a two- dimensional optical lattice by performing Quantum Monte Carlo (QMC) simulations. Our model contains a repulsive interspecies interaction between the two species of bosons and a hopping term between nearest neighbors. The phase diagram shows magnetic orderings, insulatings and superfluid phases as a function of doping for balanced populations. We predict the appearance of a first order phase transition from an antiferromagnetic phase to a superfluid phase near half filling. A phase transition from superfluid to an exotic phase occurs away from half filling at very low temperature.   

An Anomalously Elastic, Intermediate Phase in Randomly Layered Planar Magnets, Superfluids, and Superconductors

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.   

Quantum fidelity in the thermodynamic limit

A quantum phase transition happens when dramatic changes in the ground state properties of a quantum system can be induced by a tiny variation of an external parameter (e.g., a magnetic field in spin systems). Quantum fidelity -- the overlap between two ground states calculated at slightly different values of the external parameter -- provides the most basic probe into the dramatic change of the wave-function. In this talk I will discuss quantum fidelity focusing on thermodynamic regime. I will present novel analytical results for quantum fidelity of the Ising chain, a paradigmatic model of quantum phase transitions, and discuss a theory extending these findings to systems characterized by other universality classes. In particular, I will show how quantum fidelity approaches a non-analytic limit, quantify how the Anderson catastrophe takes place in quantum critical systems, and discuss scaling properties of quantum fidelity when it cannot be approximated by the popular fidelity susceptibility approach. This approach provides a promising way of characterizing quantum phase transition in strongly correlated systems. The work is summarized in M.M. Rams, B. Damski, arXiv:1010:1048   

Finite-Temperature Fidelity Susceptibility for One-Dimensional Quantum Systems

We calculate the fidelity susceptibility $\chi_f$ for the Luttinger model and show that there is a universal contribution linear in temperature $T$ (or inverse length $1/L$) by using conformal field theory. Furthermore, we develop an algorithm - based on a lattice path integral approach - to calculate the fidelity $F(T)$ in the thermodynamic limit for one-dimensional quantum systems. We check the Luttinger model predictions by calculating $\chi_f(T)$ analytically for free spinless fermions and numerically for the $XXZ$ chain. Finally, we study $\chi_f$ at the two phase transitions in this model.\\*[0.2cm] J. Sirker, PRL {\bf 105}, 117203 (2010)   

Thermodynamics of itinerant metamagnetic transitions

Itinerant metamagnetic transitions may be driven by features in the electronic density of states. These features produce signatures in the entropy and specific heat near to the transition. We study these signatures for a variety of different cases, identifying the key features which differ from naive expectations, such as enhanced critical fields and `non-Fermi liquid' temperature dependencies above the transition. We will consider the generic case of a logarithmically divergent density of states, as caused by a van Hove singularity in 2D. We also study a specific model for the bandstructure of Sr$_3$Ru$_2$O$_7$, a material with a well-studied metamagnetic transition and quantum critical endpoint. We consider how far the behaviour of the system can be explained by the density of states rather than quantum fluctuations, and the distinctive features of this mechanism. The most intriguing feature of Sr$_3$Ru$_2$O$_7$ is an unusual phase with a higher entropy than its surroundings, we consider how this may arise in the context of a density of states picture and find that we can reproduce the observed thermodynamic behaviour and first-order phase transitions.   

Low-energy behavior of the generalized Golden chain at an integrable point

Recently, properties of collective states of interacting non-Abelian anyons have attracted a considerable attention. In particular, it has been shown to that the generalization of the Golden chain, a chain of interacting Fibonacci anyons, has a rich phase diagram with various critical and gapped phases. In additions, several integrable points have also been studied. We identify a new integrable point in the parameter space of the model and diagonalize the Hamiltonian exactly using the Bethe Ansatz method. To describe the corresponding low-energy conformal field theory, we perform the finite-size analysis to calculate the central charge and critical exponents.   

Tensor renormalization group: Local magnetizations, correlation functions, and phase diagrams of systems with quenched randomness

The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched randomness, is extended in this study to systems with quenched randomness [1]. Local magnetizations and correlation functions as a function of spin separation are calculated as tensor products subject to renormalization-group transformation. Phase diagrams are extracted from the long-distance behavior of the correlation functions. The approach is illustrated with the quenched bond-diluted Ising model on the triangular lattice. An accurate phase diagram is obtained in temperature and bond-dilution probability for the entire temperature range down to the percolation threshold at zero temperature.\\[4pt] [1] C. G\"uven, M. Hinczewski, and A.N. Berker, Phys. Rev. E 82, 051110 (2010).   

Nature of Fermi Systems near l=0 Pomeranchuk Instability: A Tractable Crossing Symmetric Equation Approach

In Fermi liquids, a Pomeranchuk instability occurs when one of the Landau parameters $F^{a,s}_{\ell} \rightarrow -(2\ell+1)$. The Pomeranchuk instabilities at $F^{a,s}_0 = -1$ are related to respectively to a ferromagnetic transition ($a$), and to a density wave or charge instability resulting in phase separation ($s$). We use the tractable crossing symmetric equations (TSCE) method to explore the nature of quantum fluctuations, excitations and pairing in a 3D Fermi system, around these points. We obtain interesting limiting results at zero and finite momentum (q), and in the limits of large and small coupling strengths. We develop methods to deal with a set of finite-q singularities in the competing quantum fluctuation terms contained in TSCE; these may have physical significance. Using graphical and numerical methods to solve coupled non-linear integral equations that arise in the TSCE scheme, we obtain results for the behavior of spin and density excitations, and pairing properties around the instability points. Our results may have relevance to ferromagnetic superconductors.   

Microscopic model for the Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ Ruddlesden-Popper series of materials

The Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ family of materials displays an insulator to metal transition as the number of layers (n) increases. The presence of large spin-orbit coupling is believed to be a significant ingredient for the novel J$_{eff}= 1/2$ state found in Sr$_{2}$IrO$_{4}$. We offer a microscopic tight-binding Hamiltonian with spin-orbit coupling and Hubbard interactions, and compare our results with experimentally observed phases.   

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order-parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics.   

Quantum antiferromagnet on a Bethe lattice at percolation I. Low-energy states, DMRG, and diagnostics

We investigate ground and excited state properties of randomly diluted spin-1/2, exchange-coupled Heisenberg antiferromagnets on the Bethe lattice with coordination 3. In the case of square lattice percolation clusters, previous Quantum Monte Carlo (QMC) calculations [1] found that the singlet-triplet gaps scaled ``anomalously,'' being much smaller than the $1/N$ scaling expected from the tower of ``quantum rotor'' states (due to $E=M^2/2N\chi$). The low energies were attributed to the interaction of distant ``dangling spins,'' forced by the local imbalance of even and odd sites. In the present study we further study this effect on the Bethe lattice, using Exact Diagonalization and density-matrix RG. (DMRG applies naturally since the Bethe lattice lacks loops). We introduce inter-site correlation and susceptibility matrices as diagnostics to identify the spatial locations of the low-energy degrees of freedom, and to understand interactions between them. These matrices have been computed within the harmonic spin-wave theory, in order to highlight the deviations seen in the spin-1/2 system. In addition to the above, we propose a simple effective Hamiltonian which explains the magnitude of the singlet-triplet gap. \\[4pt] [1] L. Wang and A. Sandvik, Phys. Rev. B 81, 054417 (2010).   

Quantum antiferromagnet on a Bethe lattice at percolation II.Effective Hamiltonian for dangling spins

The lowest energy excitations of spin 1/2 Heisenberg antiferromagnets on percolation clusters (about the Neel ordered state) were believed to be ``quantum rotor states'' scaling with cluster size as 1/N, until Wang and Sandvik [Wang et al, Phys. Rev. B 81, 054417 (2010)] discovered a class of states in the diluted square lattice that had even lower energies and had a different finite size scaling of the gap exponent. They conjectured these anomalous states were due to local even/odd sublattice imbalances, leading to emergent local moments called ``dangling spins'' that interact over large distances, mediated through intervening spins. We have pursued this question on the z=3 Bethe lattice at the percolation threshold. Exact diagonalization shows, forevery cluster, a split-off group of low-energy states having the same quantum numbers as can be made using the dangling spins. We identify these with the Wang-Sandvik anomalous states and model their energies using an effective pair Hamiltonian coupling the ``dangling spins.'' The couplings are a function of separation and geometry; the parameters are solved by fitting to a database of different clusters.The separation dependence of these interactions can be related to the gap scaling with N. We will also compare the effective Hamiltonian predictions to the intersite susceptibility matrix of each cluster.