This book is a course in modern quantum field theory as seen through the eyes of a theorist working in condensed matter physics. It contains a gentle introduction to the subject and therefore can be used even by graduate students. The introductory parts include a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals including a discussion of Landau–Fermi liquid theory. In later chapters the discussion gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.

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We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains (spin ladder). It is shown that the system always has a spectral gap. For the case of identical chains the model in the continuous limit is shown to be equivalent to four decoupled non-critical Ising models with the Z 2 ×SU(2)-symmetry. For this case we obtain the exact expressions for asymptotics of spin-spin correlation functions. It is shown that when the chains have different exchange integrals J 1 >> J 2 the spectrum at low energies is described by the O(3)-nonlinear sigma model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility.cond-mat/9508047

We investigate the phase transitions in two-legs ladder systems in the incommensurate phase, for which the gap is destroyed by a magnetic field (hc1 < h) and the ladder is not yet totally saturated (h < hc2). We compute quantitatively the correlation functions as a function of the magnetic field for an isolated strong coupling ladder J ⊥ ≫ J and use it to study the phase transition occuring in a three dimensional array of antiferromagnetically coupled ladders. The three dimensional ordering is in the universality class of Bose condensation of hard core bosons. We compute the critical temperature Tc(h) as well as various physical quantities such as the NMR relaxations rate. Tc has an unusual camel-like shape with a local minimum at h = (hc1 +hc2)/2 and behaves as Tc ∼ (h−hc1) 2/3 for h ∼ hc1. We discuss the experimental consequences for compounds such as Cu2(C5H12N2)2Cl4 be found in section V and some technical details are left for the Appendix.

The ground-state ordering and dynamics of the two-dimensional (2D) S=1/2 frustrated Heisenberg antiferromagnet Cs2CuCl4 is explored using neutron scattering in high magnetic fields. We find that the dynamic correlations show a highly dispersive continuum of excited states, characteristic of the RVB state, arising from pairs of S=1/2 spinons. Quantum renormalization factors for the excitation energies (1.65) and incommensuration (0.56) are large.The concept of fractional quantum states is central to the modern theory of strongly correlated systems. In magnetism, the most famous example is the spin S=1/2 1D Heisenberg antiferromagnetic chain (HAFC) where pairs of S=1/2 spinons are deconfined from locally allowed S=1 states; a phenomenon that is now well established both theoretically [1] and experimentally [2]. These spinons are topological excitations identified with quantum domain walls. Experimentally, such fractionalization is manifest as a highly dispersive continuum in the dynamical magnetic susceptibility measured by e.g. neutron scattering [2], and for the HAFC identified as creation of pairs of spinons.In 1973 Anderson [3] suggested that a 2D fractional quantum spin liquid may take the form of a "resonating valence bond" (RVB) state comprising singlet spin pairings in the ground state, and with pairs of excited S=1/2 spinons separating via rearrangement of those bonds. The dominant feature of the RVB state, present in all its theoretical descriptions [4][5][6] is an extended, highlydispersive, continuum. To date this feature remains unobserved in any 2D magnet; in the case of the S=1/2 Heisenberg square lattice (HSL) mean field confining effects lead to S=1 magnons and a renormalized classical picture of fluctuations around local Néel order emerges [7,8]. One may think, however, that because frustrating interactions can counteract the staggered fields responsible for confinement [8,9], they may provide a route to generating fractional phases in 2D.We explore such a scenario by making neutron scattering studies on Cs 2 CuCl 4 . By exploiting its unique experimental properties as a low-exchange quantum magnet [10] we reveal an unexpectedly strong two-dimensionality in the form of a triangular antiferromagnet with partially released frustration. The simplicity of the couplings in Cs 2 CuCl 4 makes it a model system to investigate generic features of 2D frustrated quantum antiferromagnets.The structure of Cs 2 CuCl 4 is orthorhombic (Pnma) with lattice parameters a=9.65Å, b=7.48Å and c=12.35Å at 0.3 K. Magnetic interactions are mostly restricted between Cu 2+ S=1/2 spin-sites in the (b, c) plane, see Fig. 1(a), with coupling J along b ("chains") and zigzag "interchain" coupling J ′ along the c-axis [11]. A small interlayer coupling J ′′ < 10 −2 J (along a) stabilizes 3D order below T N = 0.62 K into an incommensurate structure along b due to the frustrated couplings; weak anisotropies confine the ordered moments to rotate in cycloids near coincident with the (b, c) plane, see Fig. 1(d) but with a small tilt...

Recent spectroscopic observations of a d-wave-like gap in stripe-ordered La(2-x)Ba(x)CuO(4) with x=1/8 have led us to critically analyze the anisotropic transport and magnetization properties of this material. The data suggest that concomitant with the spin ordering is an electronic decoupling of the CuO(2) planes. We observe a transition (or crossover) to a state of two-dimensional (2D) fluctuating superconductivity, which eventually reaches a 2D superconducting state below a Berezinskii-Kosterlitz-Thouless transition. Thus, it appears that the stripe order in La(2-x)Ba(x)CuO(4) frustrates three-dimensional superconducting phase order, but is fully compatible with 2D superconductivity and an enhanced T(c).

We report a combined experimental and theoretical investigation of the magnetic structure of the honeycomb lattice magnet Na2IrO3, a strong candidate for a realization of a gapless spin-liquid. Using resonant x-ray magnetic scattering at the Ir L3-edge, we find 3D long range antiferromagnetic order below TN =13.3 K. From the azimuthal dependence of the magnetic Bragg peak, the ordered moment is determined to be predominantly along the a-axis. Combining the experimental data with first principles calculations, we propose that the most likely spin structure is a novel "zig-zag" structure.

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at ν = 1 is an SU (2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU (2) Chern-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at ν = 1/2 are obtained by a fluxattachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.