K. Sengupta, S. V. Isakov, Yong Baek Kim
We study the superfluid-insulator transitions of bosons on the Kagome lattice at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We find that at f=1/2 the bosons will always be in a superfluid phase and demonstrate that the T_3 symmetry of the dual (dice) lattice, which results in dynamic localization of vortices due to the Aharanov-Bohm caging effect, is at the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons exhibit a quantum phase transition between superfluid and translational symmetry broken Mott insulating phases. We discuss the possible broken symmetries of the Mott phase and elaborate the theory of such a transition. Finally we map the boson system to a XXZ spin model in a magnetic field and discuss the properties of this spin model using the obtained results.
Yong Baek Kim
It was recently shown that dipolar composite fermions emerged from the lowest-Landau-level formulation of the quantum Hall effect give rise to similar results as those of the Chern-Simons gauge theory in the long wavelength and low energy limit. We ask whether this correspondence is still valid at finite wavevectors where the excitations do not necessarily look like dipolar quasiparticles. In particular, q=2k_F density-density response function of the compressible state at ν=1/2 is evaluated in the low energy limit within the framework of the lowest-Landau-level theory. The imaginary parts of the density-density response functions at q=2k_F of two theories have the same \sqrtω dependence. However, the coefficient of the \sqrtω term in the case of the lowest-Landau-level theory is not universal and can be much smaller than the corresponding coefficient in the Chern-Simons theory. We also discuss possible connection between these results and the recent experiment on phonon-mediated drag in the double-layer ν=1/2 system.
Yong Baek Kim, Hae-Young Kee
Nematic Fermi liquid arises when the system of interacting fermions spontaneously breaks the rotational symmetry while the translational symmetry is preserved. We consider a Nematic Fermi liquid of fermions with two distinct quantum numbers. Two quantum numbers represent the spin degrees of freedom or the layer degrees of freedom of the bilayer system. There are two director modes in this system: the in-phase and out-of-phase modes. We find that the out-of-phase (in-phase) mode mediates an attractive (repulsive) interaction between fermions with different quantum numbers. Pairing instability occurs under certain conditions when the in-phase mode is gapped due to a lattice potential. Implications to the stripe phase of Cuprates and the quantum Hall effect of two dimensional electron systems are discussed.
Yong Baek Kim, Ziqiang Wang
We study the stability of the spin gap phase in the U(1) slave-boson theory of the t-J model in connection to the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave-bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those of the strange metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum critical and quantum disordered regime of the boson system. We also show that the regime of quantum disordered bosons with the paired fermions can be regarded as the strong coupling version of the recently proposed nodal liquid theory.
Yong Baek Kim
We study the localization of fermions in an anisotropic random magnetic field in two dimensions. It is assumed that the randomness in a particular direction is stronger than those in the other directions. We consider a network model of zero field contours, where there are two types of randomness - the random tunneling matrix element at the saddle points and unidirectional random variation of the number of fermionic states following zero field contours. After averaging over the random complex tunneling amplitude, the problem is mapped to an SU(2N) random exchange quantum spin chain in the $N \to 0$ limit. We suggest that the fermionic state becomes critical in an anisotropic fashion.
Hae-Young Kee, Yong Baek Kim
It is shown that metamagnetic transition in metals can occur via the formation of electronic nematic order. We consider a simple model where the spin-dependent Fermi surface instability gives rise to the formation of an electronic nematic phase upon increasing the applied Zeeman magnetic field. This leads to two consecutive metamagnetic transitions that separate the nematic phase from the low-field and high-field 'isotropic' metallic phases. Possible connection to the physics of the bilayer Ruthenate, Sr$_3$Ru$_2$O$_7$, is also discussed.
Li Ern Chern, Finn Lasse Buessen, Yong Baek Kim
Recently, the observation of large thermal Hall conductivities in correlated insulators with no apparent broken symmetry have generated immense interest and debates on the underlying ground states. Here, considering frustrated magnets with bond-dependent interactions, which are realized in the so-called Kitaev materials, we theoretically demonstrate that a large thermal Hall conductivity can originate from a classical ground state without any magnetic order. We discover a novel liquid state of magnetic vortices, which are inhomogeneous spin textures embedded in the background of polarized spins, under out-of-plane magnetic fields. In the classical regime, different configurations of vortices form a degenerate manifold. We study the static and dynamical properties of the magnetic vortex liquid state at zero and finite temperatures. In particular, we show that the spin excitation spectrum resembles a continuum of nearly flat Chern bands, which ultimately leads to a large thermal Hall conductivity. Possible connections to experiments are discussed.
Wonjune Choi, Tomonari Mizoguchi, Yong Baek Kim
Topological phases in magnetic materials offer novel tunability of topological properties via varying the underlying magnetism. We show that three dimensional Kitaev materials can provide a great opportunity for controlling symmetry-protected topological nodal magnons. These materials are originally considered as strong candidates for the Kitaev quantum spin liquid due to the bond-dependent frustrating spin exchange interactions. As a concrete example, we consider the symmetry and topology of the magnons in the canted zig-zag ordered state in the hyperhoneycomb $β\text{-}\mathrm{Li_2IrO_3}$, which can be obtained by applying a magnetic field in the counter-rotating spiral state at zero field. It is shown that the magnetic glide symmetries and the non-Hermitian nature of the bosonic magnons lead to unique topological protection that is different from the case of the fermionic counterparts. We investigate how such topological magnons can be controlled by changing the symmetry of the underlying spin exchange interactions.
Finn Lasse Buessen, Yong Baek Kim
The theoretical inception of the Kitaev honeycomb model has had defining influence on the experimental hunt for quantum spin liquids, bringing unprecedented focus onto the synthesis of materials with bond-directional interactions. Numerous Kitaev materials, which are believed to harbor ground states parametrically close to the Kitaev spin liquid, have been investigated since. Yet, in these materials the Kitaev interaction often comes hand in hand with off-diagonal $Γ$ interactions -- with the competition of the two potentially giving rise to a magnetically ordered ground state. In an attempt to aid future material investigations, we study the phase diagram of the spin-1/2 Kitaev-$Γ$ model on the honeycomb lattice. Employing a pseudofermion functional renormalization group approach which directly operates in the thermodynamic limit and captures the joint effect of thermal and quantum fluctuations, we unveil the existence of extended parameter regimes with emergent incommensurate magnetic correlations at finite temperature. We supplement our results with additional calculations on a finite cylinder geometry to investigate the impact of periodic boundary conditions on the incommensurate order, thereby providing a perspective on previous numerical studies on finite systems.
Adarsh S. Patri, Yong Baek Kim
The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically investigate superconducting instabilities instigated by multipolar Kondo interactions. Employing multipolar fluctuations (mediated by RKKY interaction) coupled to conduction electrons via two-channel Kondo and novel multipolar Kondo interactions, we uncover a variety of superconducting states characterized by higher-angular momentum Cooper pairs, $J=0,1,2,3$. We demonstrate that both odd and even parity pairing functions are possible, regardless of the total angular momentum of the Cooper pairs, which can be traced back to the atypical nature of the multipolar Kondo interaction that intertwines conduction electron spin and orbital degrees of freedom. We determine that different (point-group) irrep classified pairing functions may coexist with each other, with some of them characterized by gapped and point node structures in their corresponding quasiparticle spectra. This work lays the foundation for discovery and classification of superconducting states in rare-earth metallic compounds with multipolar local moments.
Yu-Hsueh Chen, Jozef Genzor, Yong Baek Kim, Ying-Jer Kao
We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $\mathbb{Z}_2$ spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge excitations are found at $\mathbf{K}, \mathbf{K}'=(\pm2π/3, \mp 2π/3)$, with a corresponding correlation length of $ξ\approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language
Sophia Simon, Adarsh S. Patri, Yong Baek Kim
Experimental identification of quantum spin ice (QSI), a U(1) quantum spin liquid on the pyrochlore lattice hosting emergent photons, is a major challenge in frustrated magnets. In this work, we propose ultrasound measurements as a novel tool for probing the emergent photons of various QSI phases. Our analysis includes QSI phases in non-Kramers doublet compounds such as $\rm{Pr}_2 \rm{Zr}_2 \rm{O}_7$ as well as dipolar-octupolar Kramers doublet compounds such as $\rm{Ce}_2 \rm{Zr}_2 \rm{O}_7$. The latter may host emergent photons associated with an octupolar component which renders them difficult to detect with inelastic neutron scattering. We demonstrate theoretically how the speed of the emergent photons can be obtained from the renormalization of the phonon spectrum and show that ultrasound measurements provide a means of distinguishing the dipolar from the octupolar QSI phase in dipolar-octupolar materials.
Heqiu Li, Yong Baek Kim, Hae-Young Kee
Recent experiments on Kitaev spin liquid candidate materials reported non-monotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the phase transitions between different flux sectors as a function of the magnetic field. The thermal conductivity due to Majorana fermions shows dip-bump structures as the magnetic field increases, which is caused by either the transitions between different flux sectors of Kitaev spin liquids or the topological transitions that change the Majorana Chern number within the same flux sector. It is shown that the change of Chern number is closely related to the four-Majorana-fermion interaction induced by the magnetic field. The non-monotonic behavior in thermal conductivity emerges at finite temperature, and it becomes weaker when temperature decreases towards zero. Our model provides a generic mechanism for the Kitaev spin liquids to develop non-monotonic magnetic-field dependence of thermal conductivity while the detailed comparison to realistic materials remains an open question for future investigation.
SangEun Han, Daniel J. Schultz, Yong Baek Kim
Notable non-Fermi liquid and quantum critical behaviors are observed in rare-earth metallic systems with non-Kramers local moments supporting a number of different multipolar moments. A prominent example is $\text{Pr(Ti,V)}_{2}\text{Al}_{20}$, where the non-Kramers doublet of the $\text{Pr}^{3+}$ ion allows quadrupolar and octupolar moments, but lacks a dipolar moment. Previous theoretical studies show that a single impurity Kondo problem with such an unusual local moment leads to novel non-Fermi liquid states. In this work, we investigate possible quantum critical behaviors arising from the competition between non-Fermi liquid states and multipolar-ordered phases induced by the RKKY interaction. We consider a local version of the corresponding Kondo lattice model, namely the Bose-Fermi Kondo model. Here, the multipolar local moments are coupled to fermionic and bosonic bath degrees of freedom representing the multipolar Kondo effect and RKKY interactions. Using a perturbative renormalization group (RG) study up to two loop order, we find critical points between non-Fermi liquid Kondo fixed points and a quadrupolar ordered fixed point. The critical points describe quantum critical behaviors at the corresponding phase transitions and can be distinguished by higher order corrections in the octupolar susceptibility that can be measured by ultrasound experiments. Our results imply the existence of a rich expansion of the phases and quantum critical behaviors in multipolar heavy fermion systems.
Prashant Kumar, Yong Baek Kim, S. Raghu
The integer quantum Hall to insulator transition (IQHIT) is a paradigmatic quantum critical point. Key aspects of this transition, however, remain mysterious, due to the simultaneous effects of quenched disorder and strong interactions. We study this transition using a composite fermion (CF) representation, which incorporates some of the effects of interactions. As we describe, the transition also marks a IQHIT of CFs: this suggests that the transition may exhibit `self-duality'. We show the explicit equivalence of the electron and CF Lagrangians at the critical point via the corresponding non-linear sigma models, revealing the self-dual nature of the transition. We show analytically that the resistivity tensor at the critical point is $ρ^c_{xx} = ρ^c_{xy} = \frac{h}{e^2}$, which are consistent with the expectations of self-duality, and in rough agreement with experiments.
Adarsh S. Patri, Masashi Hosoi, SungBin Lee, Yong Baek Kim
Multipolar magnetism is an emerging field of quantum materials research. The building blocks of multipolar phenomena are magnetic ions with a non-Kramers doublet, where the orbital and spin degrees of freedom are inextricably intertwined, leading to unusual spin-orbital entangled states. The detection of such subtle forms of matter has, however, been difficult due to a limited number of appropriate experimental tools. In this work, motivated by a recent magnetostriction experiment on Pr$_2$Zr$_2$O$_7$, we theoretically investigate how multipolar quantum spin ice, an elusive three dimensional quantum spin liquid, and other multipolar ordered phases in the pyrochlore materials can be detected using magnetostriction. We provide theoretical results based on classical and/or quantum studies of non-Kramers and Kramers magnetic ions, and contrast the behaviors of distinct phases in both systems. Our work paves an important avenue for future identification of exotic ground states in multipolar systems.
Hyun-Yong Lee, Naoki Kawashima, Yong Baek Kim
Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the renowned $S$=$1/2$ model. On the other hand, the nature of the ground state remains elusive since the $S$=$1$ model is not exactly solvable in contrast to the $S$=$1/2$ model. In this work, we construct a tensor network ground state wavefunction for the S=1 Kitaev model, which is explicitly written in terms of physical spin operators. We explain how this class of wavefunctions can be successfully used for variational computations and compare the outcomes to known results on finite size systems. We establish the existence of distinct topological sectors on torus by constructing the minimally entangled states in the degenerate ground state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the S=1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles.
Félix Desrochers, Li Ern Chern, Yong Baek Kim
Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ansätze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ansätze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $π$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $π/2$- and $3π/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.
Gang Chen, Yong Baek Kim
We present a theory for the metal-insulator transition (MIT) in the quantum-spin-liquid candidate material Na4Ir3O8. We consider an extended Hubbard model on the hyperkagome lattice, which incorporates atomic spin-orbit coupling (SOC) and multi-orbital interactions of iridium 5d electrons. This model is analyzed using the slave-rotor mean-field theory and thermodynamic properties across the MIT are studied. The ground state in the insulating side is a U(1) quantum spin liquid with spinon Fermi surfaces that consist of multiple particle-like and hole-like pockets. It is shown that the Wilson ratio in the quantum spin liquid phase is highly enhanced compared to the metallic state. This originates from the fact that the magnetic susceptibility in the quantum spin liquid phase acquires multiple enhancements due to the strong SOC, reduced band-width and on-site spin-orbital exchange, while the heat capacity does not change much across MIT. This explains the large Wilson ratio of the insulating phase observed in the previous experiment on Na4Ir3O8. Possible connections to other existing and future experiments, in particular on the metallic phase, are discussed.
Eric Kin-Ho Lee, Robert Schaffer, Subhro Bhattacharjee, Yong Baek Kim
Motivated by recent experiments on $β-$Li$_2$IrO$_3$, we study the phase diagram of the Heisenberg-Kitaev model on a three dimensional lattice of tri-coordinated Ir$^{4+}$, dubbed the hyperhoneycomb lattice by Takagi et. al. The lattice geometry of this material, along with Ir$^{4+}$ ions carrying $J_{\rm eff}=1/2$ moments, suggests that the Heisenberg-Kitaev model may effectively capture the low energy spin-physics of the system in the strong-coupling limit. Using a combination of semiclassical analysis, exact solution and slave-fermion mean field theory, we find, in addition to the spin-liquid, four different magnetically ordered phases depending on the parameter regime. All four magnetic phases--the Néel, the polarized ferromagnet, the skew-stripy and the skew-zig-zag, have collinear spin ordering. The three dimensional Z$_2$ spin liquid, which extends over an extended parameter regime around the exactly solvable Kitaev point, has a gapless Majorana mode with a deformed Fermi-circle (co-dimensions, $d_c=2$). We discuss the effect of the magnetic field and finite temperature on different phases that may be relevant for future experiments.