These lectures review the large N Schwinger Bosons Mean Field approach to the quantum Heisenberg model. The method applies to ordered and disordered phases in all dimensions, at zero and at finite temperature. Extension to frustrated models is explained. An example for an experimentally useful application, is the temperature dependent staggered magnetization of the layered antiferromagnet.
Resorting to the Schwinger-boson representation for the description of a localized magnetic-impurity state, we develop an RG-improved (renormalization group) perturbation theory for the Kondo effect. This Schwinger-boson based RG-improved perturbation theory covers the whole temperature range from a decoupled local moment state to a local Fermi-liquid state through the crossover temperature regime, shown from the specific heat and spin susceptibility of the magnetic impurity. The Schwinger-boson based RG-improved perturbation theory makes the strong coupling fixed point at IR (infrared) access…
We apply the dynamical large-$N$ Schwinger boson technique as an impurity solver for the dynamical mean-field theory (DMFT) calculations of the Kondo lattice model. Our approach captures the hybridization physics through the DMFT self-consistency that is missing in the pure Schwinger boson calculations with independent electron baths. The resulting thermodynamic and transport properties are in qualitative agreement with more rigorous calculations and give the correct crossover behavior over a wide temperature range from the local moment regime to the Fermi liquid. Our method may be further ext…
$Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
We have studied the effect of the Dzyaloshinskii-Moriya interaction on kagome Heisenberg anti-ferromagnet using Schwinger boson mean field theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ansätze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and…
We employ the functional renormalization group to investigate the phase diagram of the $t-t'$ Hubbard model on the square lattice with finite chemical potential $μ$ at zero temperature. A unified scheme to derive flow equations in the symmetric and symmetry broken regimes allows a consistent continuation of the renormalization flow in the symmetry broken regimes. At the transition from the symmetric regime to the symmetry broken regimes, our calculation reveals leading instabilities in the d-wave superconducting and antiferromagnetic channels. Furthermore, we find a first order transition betw…
We excite the vacuum of a relativistic theory of bosons coupled to a $U(1)$ gauge field in 1+1 dimensions (bosonic Schwinger model) out of equilibrium by creating a spatially separated particle-antiparticle pair connected by a string of electric field. During the evolution, we observe a strong confinement of bosons witnessed by the bending of their light cone, reminiscent of what has been observed for the Ising model [Nat. Phys. 13, 246 (2017)]. As a consequence, for the time scales we are able to simulate, the system evades thermalization and generates exotic asymptotic states. These states a…
Quantum Dynamics of Multiferroic Helimagnets: a Schwinger-Boson Approach
我们研究的量子动力学/波动的摆线螺旋磁铁的Schwinger玻色子方法。与经典涨落形成鲜明对比的是，量子涨落本质上是共线的，这使得随着温度的降低，共线自旋密度波态略高于螺旋摆线态。从这个角度讨论了螺旋线的约化椭圆比、中子散射和红外吸收光谱等物理性质，并讨论了它们与准一维LiCu $_2$ O $_2$和LiCuVO $_4$的可能关系.
Strange metal behavior arises in heavy fermion metals close to antiferromagnetic transitions. An increasing amount of experiments indicates a link of such behavior to a Kondo breakdown quantum critical point. To shed light on this intriguing problem, we study the 2D Kondo-Heisenberg model using a dynamical large-N multichannel Schwinger boson approach. We identify and characterize the quantum phase transition from an antiferromagnetically ordered ground state to a Kondo-dominated paramagnetic state, and attribute a jump in certain phase shift to Kondo breakdown. In addition, we calculate trans…
We study possible spin liquids on square lattice that respect all lattice symmetries and time-reversal symmetry within the framework of Schwinger boson (mean-field) theory. Such spin liquids have spin gap and emergent Z_2 gauge field excitations. We classify them by the projective symmetry group method, and find six spin liquid states that are potentially relevant to the J_1-J_2 Heisenberg model. The properties of these states are studied under mean-field approximation. Interestingly we find a spin liquid state that can go through continuous phase transitions to either the Néel magnetic order …
The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to…
Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
Vienna University of Technology（维也纳工业大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体的研究所）；Arnold Sommerfeld Center for Theoretical Physics, Center for NanoScience, and Munich Center for Quantum Science and Technology, Ludwig-Maximilians-Universität München（慕尼黑大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Universität Tübingen（蒂宾根大学）；Ruhr-University Bochum（波鸿鲁尔大学）；Harvard University（哈佛大学）
We use Schwinger boson mean field theory (SBMFT) to study the ground state of the spin-$S$ triangular-lattice Heisenberg model with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic interactions. Previous work on the $S=1/2$ model leads us to consider two spin liquid Ansätze, one symmetric and one nematic, which upon spinon condensation give magnetically ordered states with 120$^{\circ}$ order and collinear stripe order, respectively. The SBMFT contains the parameter $κ$, the expectation value of the number of bosons per site, which in the exact theory equals $2S$. For $κ=1$ …
Using Schwinger-boson mean-field theory, we calculate the dynamic spin structure factor at low temperatures $0<T\ll J$ for the spin-$1/2$ antiferromagnetic Heisenberg kagome model, within the gapped $\mathbb{Z}_2$ spin liquid phase Ansatz. We find that the spectral gap rapidly fills with temperature, with robust low-energy spectral weight developing by a temperature of $Δ/3$, where the spin gap is $2Δ$ (i.e., $Δ$ is the spinon gap), before any appreciable rise in spinon density or change in zero-temperature mean-field parameters. This is due to deconfinement of spinons which leads to terms sup…
Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ansätze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities…
We compute the zero temperature dynamical structure factor $S({\bf q},ω)$ of the triangular lattice Heisenberg model (TLHM) using a Schwinger boson approach that includes the Gaussian fluctuations ($1/N$ corrections) of the saddle point solution. While the ground state of this model exhibits a well-known 120$^{\circ}$ magnetic ordering, experimental observations have revealed a strong quantum character of the excitation spectrum. We conjecture that this phenomenon arises from the proximity of the ground state of the TLHM to the quantum melting point separating the magnetically ordered and spin…
Using an adaptation of Schwinger boson mean field theory (SBMFT) for nonuniform systems, we study the nature of low-energy spin excitations on the square and Bethe lattice at their percolation threshold. The optimal SBMFT parameters are interpreted as on-site potentials and pairing amplitudes, which enables an explanation of why emergent local moments develop in this system on dilution [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); H.J. Changlani et al., ibid 111, 157201 (2013)] and why the corresponding single particle frequencies are driven to anomalously low values. We disc…
Order-by-disorder from Schwinger bosons in a frustrated honeycomb ferromagnet
Institut Néel, Université Grenoble Alpes and CNRS（内尔研究所，格勒诺布尔阿尔卑斯大学和法国国家科学研究中心）；Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid（凝聚态物理理论系，凝聚态物理中心（IFIMAC）和尼古拉斯·卡布雷拉研究所，马德里自治大学）
We find that the Schwinger Boson mean field theory(SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-$\frac{1}{2}$ triangular lattice antiferromagnetic Heisenberg model(spin-$\frac{1}{2}$ TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as …
We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D long-range interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phas…
Motivated by the recent numerical evidence[1] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to Z$_2$ gauge field. We apply the projective symmetry group(PSG) method to classify possible Z$_2$ spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant Z$_2$ states, differed by the value of gauge flux, zero or $π…
Recently, uncovering the sources of thermal Hall effect in insulators has become an important issue. In the case of ferromagnetic insulators, it is well known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal Hall effect. Specifically, the DM vector parallel to the magnetization direction induces complex magnon hopping amplitudes, so that magnons act as if they feel Lorentz force. However, the DM vector which is orthogonal to the magnetization direction has hitherto been neglected as a possible source of magnon thermal Hall effect. This is because they play no role in the l…
Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
Department of Physics and Astronomy, University of Delaware（特拉华大学物理与天文学系）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；Department of Mathematical Sciences, University of Delaware（特拉华大学数学科学系）
