Discoveries of ratios whose values are constant within broad classes of materials have led to many deep physical insights. The Kadowaki-Woods ratio (KWR) 1,2 compares the temperature dependence of a metals resistivity to that of its heat capacity; thereby probing the relationship between the electronelectron scattering rate and the renormalisation of the electron mass. However, the KWR takes very different values in different materials 3,4 . Here we introduce a ratio, closely related to the KWR, that includes the effects of carrier density and spatial dimensionality and takes the same (predicted) value in organic charge transfer salts, transition metal oxides, heavy fermions and transition metalsdespite the numerator and denominator varying by ten orders of magnitude.Hence, in these materials, the same emergent physics is responsible for the mass enhancement and the quadratic temperature dependence of the resistivity and no exotic explanations of their KWRs are required.In a Fermi liquid the temperature dependence of the electronic contribution to the heat capacity is linear, i.e., C el (T ) = γT . Another prediction of Fermi liquid theory 5 is that, at low temperatures, the resistivity varies as ρ(T ) = ρ 0 + AT 2 . This is observed experimentally when electron-electron scattering, which gives rise to the quadratic term, dominates over electron-phonon scattering.Rice observed 1 that in the transition metals A/γ 2 ≈ a T M = 0.4 µΩ cm mol 2 K 2 /J 2 (Fig. 1), even though γ 2 varies by an order of magnitude across the materials he studied. Later, Kadowaki and Woods 2 found that in many heavy fermion compounds A/γ 2 ≈ a HF = 10 µΩ cm mol 2 K 2 /J 2 (Fig. 1), despite the large mass renormalisation which causes γ 2 to vary by more than two orders of magnitude in these materials. Because of this remarkable

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-1/2 triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a threesublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find roton-like minima at special wave-vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [cond-mat/0608002]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a non-linear sigma model description of the finite-temperature properties is only applicable at extremely low temperatures.

We investigate boundary critical phenomena from a quantum information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Rényi entropy Sα, which includes the von Neumann entropy (α → 1) and the single-copy entanglement (α → ∞) as special cases. We identify the contribution from the boundary entropy to the Rényi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g-theorem, can be regarded as a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same. Recently much work has been done to understand entanglement in quantum many-body systems. In particular, the behavior of various entanglement measures at or near a quantum phase transition [1] has received a lot of attention [2,3,4,5,6,7,8,9]. These entanglement measures include the von Neumann entropy and the single-copy entanglement, among others. The former is the most studied measure and quantifies entanglement in a bipartite system in the so-called asymptotic regime [10], whereas the latter was recently suggested to quantify the entanglement present in a single copy [9]. For a system in a pure state |ψ (e.g. the ground state) that is partitioned into two subsystems A and B, the von Neumann entropy is S 1 ≡ −Tr A ρ A log 2 ρ A where ρ A = Tr B |ψ ψ| is the reduced density matrix for A, and the single-copy entanglement is S ∞ ≡ − log 2 λ 1 , where λ 1 is the largest eigenvalue of ρ A .Studies of the von Neumann entropy for quantum spin chains [3,4,5,6,7,8] have revealed that its dependence on the size ℓ of the block A is very different for noncritical and critical systems. For the former, the von Neumann entropy increases logarithmically with ℓ until it saturates when ℓ becomes of order the correlation length ξ, while for the latter (having ξ = ∞) it diverges logarithmically with ℓ. Remarkably, the prefactor of the logarithmic term is universal and proportional to the central charge of the underlying conformal field theory (CFT) [6,11]. Furthermore, it has been shown numerically [12] that the entanglement loss along the (bulk) renormalization group (RG) flows, which is consistent with the CFT predictions for the von Neumann entropy [6,11] and with Zamolodchikov's c-theorem [13], can be given a more "fine-grained" characterization in terms of the majorization concept [14]. A theoretical analysis of majorization in these systems also appeared recently [15].Boundary critical phenomena [16] in one-dimensional (1D) quantum systems (equivalently, 2D classical systems) have attracted a lot of interest, especially in the context of boundary CFT. A closely related subject is the theory of boundary perturbations of certain conformally invariant theories, so-called integrable...

We use series expansions to study the excitation spectra of spin-1=2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Néel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs 2 CuCl 4 . If the ground state is magnetically ordered, the system must have gapless magnon excitations, which at sufficiently low energies are expected to be well described by semiclassical (i.e., large-S) approaches such as spin-wave theory (SWT) and the nonlinear sigma model (NLSM). However, if the magnon dispersion at higher energies deviates significantly from the semiclassical predictions, it is possible that the proper description of the excitations, valid at all energies, is in terms of pairs of S 1=2 spinons. In this unconventional scenario, the magnon is a bound state of two spinons, lying below the two-spinon (particle-hole) continuum.In this Letter, we use series expansions to calculate the magnon dispersion of 2D frustrated S 1=2 HAFM's. Our main finding is that for the triangular lattice model (TLM) the dispersion shows major deviations from linear SWT (LSWT) at high energies (Fig. 1). We argue that these deviations can be qualitatively understood in terms of a two-spinon picture [3], provided the spinon dispersion has minima at K i =2, where K i is a magnetic Bragg vector. Based on this interpretation of the TLM spectra, we propose an explanation for the anomalous finite-temperature behavior found in high-temperature series expansion studies [4].Both qualitatively and quantitatively, the deviations from LSWT found here for the TLM are much more pronounced than those previously reported [5][6][7][8] for the high-energy spectra of the square lattice model (SLM). We point out that the deviations from SWT increase in the Néel phase, too, upon adding frustration to the SLM. We further consider the limit of our model relevant to Cs 2 CuCl 4 and show that the calculated excitation spectra are in good agreement with experiments [1].Model.-We consider a S 1=2 HAFM on an anisotropic triangular lattice, with exchange couplings J 1 and J 2 [ Fig. 2(a)]. This model interpolates among the SLM (J 1 0), TLM (J 1 J 2 ), and decoupled chains (J 2 0). Classically, the model has Néel order for J 1 J 2 =2 with q and helical order for J 1 > J 2 =2 with q arccosÿJ 2 =2J 1 , where q (2q) is the angle between

Using Abelian bosonization with a careful treatment of the Klein factors, we show that a certain phase of the half-filled two-leg ladder, previously identified as having spin-Peierls order, instead exhibits staggered orbital currents with no dimerization.