Masafumi Udagawa

The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG). MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems. Furthermore, MPRG does not rely on any variational principles and thus supports any kind of non-Hermitian systems in any dimension. As a demonstration, we present critical properties of the Yang-Lee edge singularity in one dimension as a representative non-Hermitian system.

We study a problem of interacting fractional charges with the J1-J2-J3 Ising model on a checkerboard lattice under magnetic field. As a result of the interplay between repulsive interactions and particle density tuning by a magnetic field, the fractional charges form a classical spin liquid (CSL) phase. The CSL phase is composed of degenerate spin configurations, which can be mapped to the trimer covering of dual square lattice. The CSL state shows macroscopic ground-state entropy, implying the emergence of a novel quantum spin liquid phase when quantum fluctuations are turned on. In addition to the CSL phase, the system exhibits multiple magnetization plateaus, reflecting the fertile screening processes of dimer-monomer mixtures.

In typical flat-band models, defined as nearest-neighbor tight-binding<br /> models, flat bands are usually pinned to the special energies, such as top or<br /> bottom of dispersive bands, or band crossing points. In this paper, we propose<br /> a simple method to tune the energy of flat bands without losing the exact<br /> flatness of the bands. The main idea is to add farther-neighbor hoppings to the<br /> original nearest-neighbor models, in such a way that the transfer integral<br /> depends only on the Manhattan distance. We apply this method to several lattice<br /> models including two-dimensional kagome lattice and three dimensional<br /> pyrochlore lattice, as well as their breathing lattices and non-line graphs.<br /> The proposed method will be useful for engineering flat bands to generate<br /> desirable properties, such as enhancement of $T_c$ of superconductors and<br /> non-trivial topological orders.

We study the formation of magnetic clusters in frustrated magnets in their<br /> cooperative paramagnetic regime. For this purpose, we consider the<br /> $J_1$-$J_2$-$J_3$ classical Heisenberg model on kagome and pyrochlore lattices<br /> with $J_2 = J_3=J$. In the absence of farther-neighbor couplings, $J=0$, the<br /> system is in the Coulomb phase with magnetic correlations well characterized by<br /> pinch-point singularities. Farther-neighbor couplings lead to the formation of<br /> magnetic clusters, which can be interpreted as a counterpart of<br /> topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C.<br /> Jaubert and M. Udagawa, Phys. Rev. Lett. {\bf 119}, 077207 (2017)]. The<br /> concomitant static and dynamical magnetic structure factors, respectively<br /> $\mathcal{S}({\bm{q } })$ and $\mathcal{S}({\bm{q } },\omega)$, develop half-moon<br /> patterns. As $J$ increases, the continuous nature of the Heisenberg spins<br /> enables the half-moons to coalesce into connected `star&#039; structures spreading<br /> across multiple Brillouin zones. These characteristic patterns are a dispersive<br /> complement of the pinch point singularities, and signal the proximity to a<br /> Coulomb phase. Shadows of the pinch points remain visible at finite energy,<br /> $\omega$. This opens the way to observe these clusters through (in)elastic<br /> neutron scattering experiments. The origin of these features are clarified by<br /> complementary methods: large-$N$ calculations, semi-classical dynamics of the<br /> Landau-Lifshitz equation, and Monte Carlo simulations. As promising candidates<br /> to observe the clustering states, we revisit the origin of &quot;spin molecules&quot;<br /> observed in a family of spinel oxides $AB_2$O$_4$ ($A=$ Zn, Hg, Mg, $B=$ Cr,<br /> Fe).

We study the interplay of topological bottlenecks and energetic barriers to<br /> equilibration in a Coulomb spin liquid where a short-range energetic coupling<br /> between defects charged under an emergent gauge field supplements their<br /> entropic long-range Coulomb interaction. This work is motivated by the<br /> prevalence of memory effects observed across a wide range of geometrically<br /> frustrated magnetic materials, possibly including the spontaneous Hall effect<br /> observed in Pr2Ir2O7. Our model is canonical spin-ice model on the pyrochlore<br /> lattice, where farther-neighbour spin couplings give rise to a nearest-neighbor<br /> interaction between topological defects which can easily be chosen to be<br /> unnatural or not, i.e. attractive or repulsive between defects of equal gauge<br /> charge. Among the novel features of this model are the following. After<br /> applying a field quench, a rich dynamical approach to equilibrium emerges,<br /> dominated by multi-scale energy barriers responsible for long-lived<br /> magnetization plateaux. These even allow for the metastability of a<br /> &quot;fragmented&quot; spin liquid, an elusive regime where partial order co-exists with<br /> a spin liquid. Perhaps most strikingly, the attraction produces clusters of<br /> defects whose stability is due to a combination of energetic barriers for their<br /> break-up and proximity of opposite charges along with an entropic barrier<br /> generated by the topological requirement of annihilating a defect only together<br /> with an oppositely charged counterpart. These clusters may take the form of a<br /> &quot;jellyfish&quot; spin texture, comprising an arrangement of same-sign gauge-charges,<br /> centered on a hexagonal ring with branches of arbitrary length. The ring<br /> carries a clockwise or counterclockwise circular flow of magnetisation. This<br /> emergent toroidal degrees of freedom provides a possibility for time reversal<br /> symmetry breaking with possible relevance to the spontaneous Hall effect<br /> observed in Pr2Ir2O7.

<p>The pyrochlore lattice is a paragon of magnetic frustration, where anisotropy is the name of the game. Anisotropy can take several form: single ion, bond or lattice anisotropy for example. Motivated by the recently synthesized family of breathing pyrochlores (LiInCr4O8, Ba3Yb2Zn5O11 ...), here we shall investigate the latter kind of anisotropy, and use it as an additional knob to explore new facets of frustration.</p>

We show the existence of invariant energy levels in a Kondo lattice model on<br /> an isolated complete graph, such as a triangle and a tetrahedron. These energy<br /> levels always have fixed eigenenergies $t \pm J/2$, irrespective of the<br /> configuration of localized moments ($t$ is the transfer integral of conduction<br /> electrons and $J$ is the spin-charge coupling constant). We also extend the<br /> analysis to geometrically frustrated lattices by using the complete graphs as<br /> basic building blocks. We show that the construction rule for the invariant<br /> energy levels leads to the existence condition of localized states, if the<br /> model is defined on the triangle-based line graphs, such as a kagome lattice.<br /> We further propose a procedure of engineering isolated flat bands with broken<br /> time-reversal symmetry, which are separated from other dispersive bands with<br /> finite energy gaps.

An effective Ising model for the spin-ice type Kondo lattice model is<br /> investigated by the classical Monte Carlo simulation. We clarify the magnetic<br /> phase diagram with four phases: ice-ferro, ice-(0,0,2\pi), 32-sublattice, and<br /> all-in/all-out ordered states. The result well reproduces the phase diagram of<br /> the Kondo lattice model studied previously [H. Ishizuka et al.: J. Phys. Soc.<br /> Jpn. 81 (2012) 113706], which suggests that the RKKY interactions up to third<br /> neighbors are sufficient to describe the magnetic properties of the itinerant<br /> electron model. We discuss the peculiar nature of phase transitions: the<br /> suppression of the critical temperatures down to zero temperature between two<br /> ice phases and the presence of the tricritical points on the phase boundary of<br /> the 32-sublattice ordered state.