The Dirac-like electronic structure can host a large number of competing orders in the form of mass terms. In particular, two different order parameters can be said to be dual to each other, when a static defect in one of them traps a quantum number (or "charge") of the other. We discuss that such complementary nature of the pair of the order parameters shows up in their correlation functions and dynamical properties when a quantum phase transition is driven by fluctuations of the one of the order parameters. Approaching the transition from the disordered (paramagnetic) side, the order parameter correlation function at the critical point is reduced, while such fluctuations enhance the correlation of the dual order parameter. Such complementary behaviors in the correlation function can be used to diagnose the nature of quantum fluctuations that is the driving force of the quantum phase transition.
A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson(LGW) paradigm in describing the competing phases and phase transitions of two dimensional quantum magnets. In this paper we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examp…
Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors int…
We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormaliz…
We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U(1)$ Dirac spin liquid state proposed by Y. Ran $et al.$ [Phys. Rev. Lett. $98$, $117205$ ($2007$)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance…
We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -- RKKY interaction was carried out to 1-loop order in the $ε$ expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.
Many recently discovered advanced materials, such as high-Tc cuprates, iron pnictides and several heavy-fermions, exhibit a rich phase diagram suggesting the presence of different competing interactions that would lead to various types of ordering. Nevertheless, there is not yet a clear unifying picture allowing the understanding of the detailed mechanisms that generate such competing interactions. Having such a picture, however, could quite well be at the very roots of the requirements for understanding high-Tc superconductivity in cuprates and pnictides, for instance. In this work we conside…
We discuss the problem of characterizing "quantum disordered" ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response in electron bilinears to the skyrmion density in the local antiferromagnetic order, induced by geometric phases. We also discuss the connection to topological terms obtained under situations where the electronic spectrum has a Dirac form.
We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange couplings, with antiferromagnetic $J_{1}$. The classical ground-state phase diagram obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. Employing classical Monte Carlo simulations we show that thermal fluctuations fail to lift the degeneracy of the antiferromagnetic chain phase. Interestingly, the spin-wave spec…
We consider a model of Dirac fermions in $2+1$ dimensions with dynamically generated, anticommuting SO(3) Néel and Z$_2$ Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z$_3$ vortices in the Kekulé mass, the emergent SO(4) invaria…
In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this work, we develop a theoretical framework for addressing such competing orders in an itinerant system, described by Dirac fermions strongly coupled to an O(3) nonlinear sigma model. We focus on two spatial dimensions, where upon disordering the antiferromagnetic order by quantum fluctuations the singular tunneling events also known as (anti)hedgehogs can nucleate competing singlet orders in the paramagneti…
In the presence of axial magnetic fields that can be realized in deliberately buckled monolayer graphene, quasi-relativistic Dirac fermions may find themselves in a variety of broken symmetry phases even for weak interactions. Through a detailed Hartree self-consistent numerical calculation in finite strained graphene with cylindrical and open boundaries we establish the possibility of realizing a charge-density-wave order for the spinless fermions in the presence of weak nearest-neighbor repulsion. Such an instability gives rise to a staggered pattern of average fermionic density between bulk…
Due to the interaction between topological defects of an order parameter and underlying fermions, the defects can possess induced fermion numbers, leading to several exotic phenomena of fundamental importance to both condensed matter and high energy physics. One of the intriguing outcome of induced fermion number is the presence of fluctuating competing orders inside the core of topological defect. In this regard, the interaction between fermions and skyrmion excitations of antiferromagnetic phase can have important consequence for understanding the global phase diagrams of many condensed matt…
A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative n…
The long standing controversy concerning the effect of electron - electron interaction on the electrical conductivity of an ideal graphene sheet is settled. Performing the calculation directly in the tight binding approach without the usual prior reduction to the massless Dirac (Weyl) theory, it is found that, to leading order in the interaction strength alpha =e^2/(hbar*v0), the DC conductivity sigma/sigma0=1+C*alpha is significantly enhanced with respect to the independent-electrons result sigma0, i.e. with the value C = 0.26. The ambiguity characterizing the various existing approaches is n…
Coexisting fluctuations towards various ordered states are ubiquitous in strongly correlated electronic systems. In particular, measurements of underdoped cuprate high-temperature superconductors reveal evidence for short range charge order in parallel to large superconducting fluctuations. Here we use a non-linear sigma model to describe a system with N competing orders, and calculate its transverse thermoelectric transport coefficient in the analytically tractable limit of large N . Our results, which determine the contribution of order parameter fluctuations to the Nernst signal, are approp…
Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University（斯坦福材料能源科学研究所、SLAC国家加速器实验室和斯坦福大学）；Department of Physics and Astronomy, University of California, Irvine（加州大学尔湾分校物理与天文学系）；Department of Physics, Stanford University（斯坦福大学物理系）
We study the interaction effect in a three dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instability towards forming these ordered phases. The charge density wave phase is similar as that of a Weyl semimetal while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimental…
Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension (1D). In 1D, a key ingredient to progress is Luttinger liquid theory which provides a unified description. Here we explore a promising analogous framework in two dimensions, the Dirac spin liquid (DSL), which can be constructed on several different lattices. The DSL is a version of Quantum Electrodynamics ( QED$_3$) with four flavors of Dirac fermions coupled to photons. Importantly, its excitations also include magnetic mono…
Using determinant quantum Monte Carlo (d-QMC) simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin $S^z$ conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quan…
We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $θ= π$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $θ$ can vary continuously…
We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $ε=(3-d)$ exp…
Noncollinear and noncoplanar spin textures in solids manifest themselves not only in their peculiar magnetism but also in unusual electronic and transport properties. We here report our theoretical studies of a noncoplanar order on a simple cubic lattice and its influence on the electronic structure. We show that a four-sublattice triple-Q order induces three-dimensional massless Dirac electrons at commensurate electron fillings. The Dirac state is doubly degenerate, while it splits into a pair of Weyl nodes by lifting the degeneracy by an external magnetic field; the system is turned into a W…
In this work, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (tFeSCs). While tFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic $s$-wave superconductivity, our theory implies that such common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for tFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands w…
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link …
Density functional theory calculations with an on-site Coulomb repulsion term (GGA+U method) reveal competing ground states in (111) oriented (LaAlO$_3$)$_M$/(SrTiO$_3$)$_N$ superlattices with n-type interfaces, ranging from spin, orbital polarized, Dirac point Fermi surface to charge ordered flat band phases. These are steered by the interplay of (i) Hubbard U, (ii) SrTiO$_3$ quantum well thickness and (iii) crystal field spitting tied to in-plane strain. In the honeycomb lattice bilayer case N=2 under tensile strain inversion symmetry breaking drives the system from a ferromagnetic Dirac poi…
We report the magnetic and electrical transport properties of the bulk polycrystalline NGSMO (x ~ 0.0, 0.04, 0.08, 0.12, 0.16, 0.20, 0.25, 0.30, 0.35 and 0.42) synthesized by solid state reaction at 1350 degree Celsius. All the samples are single phase and have grain size ~1-2 micrometer. The variation of magnetic and magnetotransport properties as a function of the variance sigma^2 show some interesting trends. As sigma^2 increases, the paramagnetic-ferromagnetic (PM-FM) transition shows a gradual decrease and broadening, while the decrease in insulator metal transition (IMT) is accompanied b…
We study Skyrmion quantum numbers, charge and statistics, in (2+1) dimension induced by quadratic band toucing(QBT) fermions. It is shown that induced charge of Skyrmions is twice bigger than corresponding Dirac particles' and their statistics are always bosonic. Applying to the Bernal stacking bi-layer graphene, we show that Skyrmions of quantum spin Hall(QSH) are charge 4e bosons, so their condensation realizes charge $4e$ superconductivity(SC). The phase transition could be a second order, and one candidate theory of the transition is O(5) non linear sigma model(NLSM) with non-zero Wess-Zum…
The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with large-spin ultra-cold alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semi-metals to the gapped Mott-insulating phases in the SU(4) an…
We study the phase diagram of an effective model of competing nematic and antiferromagnetic orders of interacting electrons on the Bernal-stacked honeycomb bilayer, as relevant for bilayer graphene. In the noninteracting limit, the model features a semimetallic ground state with quadratic band touching points at the Fermi level. Taking the effects of short-range interactions into account, we demonstrate the existence of an extended region in the mean-field phase diagram characterized by coexisting nematic and antiferromagnetic orders. By means of a renormalization group approach, we reveal tha…
Nonlinear $σ$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$-dimensional spacetim…
Dirac-like fermions anomalous magneto-transport in a spin-polarized oxide two-dimensional electron system
CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Department of Physics, University of Naples Federico II（那不勒斯费德里科二世大学物理系）；Department of Physics, Universitá degli studi di Salerno（萨莱诺大学物理系）；Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS and Université de Strasbourg（斯特拉斯堡材料物理与化学研究所）
We study the order-from-disorder transition and reentrant magnetism in La(2-x)Sr(x)Cu(1-z)Zn(z)O(4) within the framework of a long-wavelength nonlinear sigma model that properly incorporates the Dzyaloshinskii-Moriya and XY anisotropies. Doping with nonmagnetic impurities, such as Zn, is considered according to classical percolation theory, whereas the effect of Sr, which introduces charge carriers into the CuO(2) planes, is described as a dipolar frustration of the antiferromagnetic order. We calculate several magnetic, thermodynamic, and spectral properties of the system, such as the antifer…
Heavy fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum non-linear sigma model, and show that the skyrmion defects of the…
We canonically quantize $O(D+2)$ nonlinear sigma models (NLSMs) with theta term on arbitrary smooth, closed, connected, oriented $D$-dimensional spatial manifolds $\mathcal{M}$, with the goal of proving the suitability of these models for describing symmetry-protected topological (SPT) phases of bosons in $D$ spatial dimensions. We show that in the disordered phase of the NLSM, and when the coefficient $θ$ of the theta term is an integer multiple of $2π$, the theory on $\mathcal{M}$ has a unique ground state and a finite energy gap to all excitations. We also construct the ground state wave fu…
The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL) which can be defined on the honeycomb, square, triangular and kagomé lattices. At low energies, the DSL on all these lattices is described by an emergent Quantum Electrodynamics (QED$_3$) with $N_f=4$ flavors of Dirac fermions cou…
Kagome lattice composed of transition-metal ions provides a great opportunity to explore the intertwining between geometry, electronic orders and band topology. The discovery of multiple competing orders that connect intimately with the underlying topological band structure in nonmagnetic kagome metals $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) further pushes this topic to the quantum frontier. Here we report the discovery and characterization of a new class of vanadium-based compounds with kagome bilayers, namely $A$V$_6$Sb$_6$ ($A$ = K, Rb, Cs) and V$_6$Sb$_4$, which, together with $A$V$_3$Sb$_5$, com…
We compute the effects of electronic interactions on gapless spin-3/2 excitations that in a noninteracting system emerge at a bi-quadratic touching of Kramers degenerate valence and conduction bands, known as Luttinger semimetal. This model can describe the low-energy physics of HgTe, gray-Sn, 227 pyrochlore iridates and half-Heuslers. For the sake of concreteness we only consider the short-range components of the Coulomb interaction. By combining mean-field analysis with a renormalization group (RG) calculation, we construct multiple cuts of the global phase diagram of interacting spin-3/2 fe…
