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Register a new userRecursion method and one-hole spectral function of the Majumdar-Ghosh model
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We consider the application of the recursion method to the calculation of one-particle Greens functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact diagonalisation of small clusters. Comparing the results for several cluster sizes allows us to establish those Lanczos coefficients that are not affected by the finite size effects and provide the information about the Greens function of the macroscopic system. The analysis of this bulk-related subset of coefficients supplemented by alternative analytic approaches allows to infer their asymptotic behaviour and to propose an approximate analytical form for the terminator of the Greens function continued fraction expansion for the infinite system. As a result, the Greens function acquires the branch cut singularity corresponding to the incoherent part of the spectrum. The method is applied to the spectral function of one-hole in the Majumdar-Ghosh model (the one-dimensional $ t-J-J^{prime}$ model at $J^{prime}/J=1/2$). For this model, the branch cut starts at finite energy $omega_0$, but there is no upper bound of the spectrum, corresponding to a linear increase of the recursion coefficients. Further characteristics of the spectral function are band gaps in the middle of the band and bound states below $omega_0$ or within the gaps. The band gaps arise due to the period doubling of the unit cell and show up as characteristic oscillations of the recursion coefficients on top of the linear increase.
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We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or $J_{1}$-$J_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behaviour of the entanglement entropy characterizing the unfrustrated Heisenberg chain as soon as $J_{2} >0.25$. This feature can be used as an indicator of the dimer phase transition that occurs at $J_{2} = J_{2}^{*} approx 0.2411 J_{1}$. Additionally, we also consider entanglement at the MG point $J_{2}=0.5 J_{1}$.
BaV3O8 contains both magnetic V4+(S=1/2) ions and non-magnetic V5+(S=0) ions. The V4+ ions are arranged in a coupled Majumdar-Ghosh chain like network. Our magnetic susceptibility chi(T) data fit well with the Curie-Weiss formula in the temperature range of 80-300K and it yields a Curie constant C=0.39cm3K/mole-V4+ and an antiferromagnetic Weiss temperature theta=-26K. The chi(T) curve shows a broad maximum at T~25K indicative of short-range order (SRO) and an anomaly corresponding to long-range order (LRO) at TN~6K. The value of the frustration index (f=mod[theta/TN]~5) suggests that the system is moderately frustrated. Above the LRO temperature the experimental magnetic susceptibility data match well with the coupled Majumdar-Ghosh chain model with the ratio of the nnn (next-nearest neighbor) to nn (nearest neighbor) magnetic coupling alpha=2 and Jnnn/kB=40K. In a mean-field approach when considering the inter-chain interactions, we obtain the total inter-chain coupling to be about 16K. The LRO anomaly at TN is also observe in the specific heat Cp(T) data and is not sensitive to an applied magnetic field up to 90kOe. A 51V NMR signal corresponding to the non-magnetic vanadium was observed. Anomalies at 6K were observed in the variation with temperature of the 51V NMR linewidth and in the spin-lattice relaxation rate 1/T1, indicating that they are sensitive to the LRO onset and fluctuations at the magnetic V sites. The existence of two components (one short and another long) is observed in the spin-spin relaxation rate 1/T2 data in the vicinity of TN. The shorter component seems to be intimately connected with the magnetically ordered state. We suggest that both magnetically ordered and non-long range ordered (non-LRO) regions coexist in this compound below the long range ordering temperature.
In this joint experimental and theoretical work magnetic properties of the Cu$^{2+}$ mineral szenicsite Cu$_3$(MoO$_4$)(OH)$_4$ are investigated. This compound features isolated triple chains in its crystal structure, where the central chain involves an edge-sharing geometry of the CuO$_4$ plaquettes, while the two side chains feature a corner-sharing zig-zag geometry. The magnetism of the side chains can be described in terms of antiferromagnetic dimers with a coupling larger than 200 K. The central chain was found to be a realization of the frustrated antiferromagnetic $J_1$-$J_2$ chain model with $J_1simeq 68$ K and a sizable second-neighbor coupling $J_2$. The central and side chains are nearly decoupled owing to interchain frustration. Therefore, the low-temperature behavior of szenicsite should be entirely determined by the physics of the central frustrated $J_1$-$J_2$ chain. Our heat-capacity measurements reveal an accumulation of entropy at low temperatures and suggest a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic $J_1$-$J_2$ spin chain, $J_2/J_1=0.5$.
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $simfrac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.
We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum-dependence of the two-particle interaction V(q). Usually, V(q) is assumed to be a constant and integrals are regularized in the ultraviolet `by hand employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense this does not affect the universal low-energy properties of the model, e.g. exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum k_F, with |k-k_F| setting a nonvanishing energy scale, the details of V(q) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum resolved spectral function as a function of energy. Even for |k-k_F| much smaller than the momentum space range of the interaction the spectral line shape depends on the details of V(q). The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi one-dimensional metals, and for recent attempts to compute the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account (nonlinear Luttinger liquid phenomenology) is discussed.
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