Construction of Many-Body Eigenstates with Displacement Transformations

Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local integrals of motion (IOM), although their actual computation has been until now a daunting task. We present a new practical computation of IOMS based on displacement transformations. It represents a general and systematic way to extend Hartree-Fock and configuration interaction theories to higher order. Our method combines minimization of energy and energy variance of a reference state with exact diagonalization. We show that our implementation is able to perform ground state calculations with high precision for relatively large systems. Since it keeps track of the IMO's forming a reference state, our method is particularly efficient dealing with excited states, both in accuracy and the number of different states that can be constructed

Emergent SO(5)SO(5) Symmetry at the N\'eel to Valence-Bond-Solid Transition

We show numerically that the `deconfined' quantum critical point between the N\'eel antiferromagnet and the columnar valence-bond-solid, for a square lattice of spin-1/2s, has an emergent $SO(5)$ symmetry. This symmetry allows the N\'eel vector and the valence-bond-solid order parameter to be rotated into each other. It is a remarkable 2+1-dimensional analogue of the $SO(4)= [SU(2)\times SU(2)]/Z_2$ symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent $SO(5)$ is strong evidence that the phase transition in the 2+1D system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (non-compact $CP^1$ model). The result indicates that in three dimensions there is an $SO(5)$-symmetric conformal field theory which has no relevant singlet operators, so is radically different to conventional Wilson-Fisher-type conformal field theories.Comment: 4+epsilon pages, 6 figure

VERTICAL TRANSMISSION OF CONSUMPTION BEHAVIOR AND THE DISTRIBUTION OF SURNAMES

This paper attempts to detect the existence of links in consumptionpreferences between generations. Preferences for consumption goods may bedetermined by the preferences of parents (vertical transmission) and/or bypreferences arising from the environment (horizontal transmission). Wepropose an indirect methodology to overcome the lack of data on consumptionchoices of dynasties, i.e., parents and their adult offspring. This new approachis based on the analysis of the correlation between the geographicaldistributions of surnames and consumption choices. Our results show that thereis horizontal transmission of preferences regarding non-food items and possiblyvertical transmission for food items.Preference formation, surnames, vertical and horizontal transmission.