Matrix Product State Description and Gaplessness of the Haldane-Rezayi State

We derive an exact matrix product state representation of the Haldane-Rezayi state on both the cylinder and torus geometry. Our derivation is based on the description of the Haldane-Rezayi state as a correlator in a non-unitary logarithmic conformal field theory. This construction faithfully captures the ten degenerate ground states of this model state on the torus. Using the cylinder geometry, we probe the gapless nature of the phase by extracting the correlation length, which diverges in the thermodynamic limit. The numerically extracted topological entanglement entropies seem to only probe the Abelian part of the theory, which is reminiscent of the Gaffnian state, another model state deriving from a non-unitary conformal field theory.Comment: Corrected labels in Fig.

Model States for a Class of Chiral Topological Order Interfaces

Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. To go beyond effective field theories, we study the prototypical example of such an interface between two Abelian states, namely the Laughlin and Halperin states. Using matrix product states, we propose a family of model wavefunctions for the whole system including both bulks and the interface. We show through extensive numerical studies that it unveils both the universal properties of the system, such as the central charge of the gapless interface mode and its microscopic features. It also captures the low energy physics of experimentally relevant Hamiltonians. Our approach can be generalized to other phases described by tensor networks.Comment: Published version. Former supplementary material has been extended and published as a separate articl

Sensory Stimulation-Dependent Plasticity in the Cerebellar Cortex of Alert Mice

In vitro studies have supported the occurrence of cerebellar long-term depression (LTD), an interaction between the parallel fibers and Purkinje cells (PCs) that requires the combined activation of the parallel and climbing fibers. To demonstrate the existence of LTD in alert animals, we investigated the plasticity of local field potentials (LFPs) evoked by electrical stimulation of the whisker pad. The recorded LFP showed two major negative waves corresponding to trigeminal (broken into the N2 and N3 components) and cortical responses. PC unitary extracellular recording showed that N2 and N3 occurred concurrently with PC evoked simple spikes, followed by an evoked complex spike. Polarity inversion of the N3 component at the PC level and N3 amplitude reduction after electrical stimulation of the parallel fiber volley applied on the surface of the cerebellum 2 ms earlier strongly suggest that N3 was related to the parallel fiber–PC synapse activity. LFP measurements elicited by single whisker pad stimulus were performed before and after trains of electrical stimuli given at a frequency of 8 Hz for 10 min. We demonstrated that during this later situation, the stimulation of the PC by parallel and climbing fibers was reinforced. After 8-Hz stimulation, we observed long-term modifications (lasting at least 30 min) characterized by a specific decrease of the N3 amplitude accompanied by an increase of the N2 and N3 latency peaks. These plastic modifications indicated the existence of cerebellar LTD in alert animals involving both timing and synaptic modulations. These results corroborate the idea that LTD may underlie basic physiological functions related to calcium-dependent synaptic plasticity in the cerebellum

Metabotropic action of postsynaptic kainate receptors triggers hippocampal long-term potentiation

Long-term potentiation (LTP) in the rat hippocampus is the most extensively studied cellular model for learning and memory. Induction of classical LTP involves an NMDA receptor- and calcium-dependent increase in functional synaptic AMPA receptors mediated by enhanced recycling of internalized AMPA receptors back to the postsynaptic membrane. Here we report a novel, physiologically relevant NMDA receptor-independent mechanism that drives increased AMPA receptor recycling and LTP. This pathway requires the metabotropic action of kainate receptors and activation of G-protein, protein kinase C and phospholipase C. Like classical LTP, kainate receptor-dependent LTP recruits recycling endosomes to spines, enhances synaptic recycling of AMPA receptors to increase their surface expression and elicits structural changes in spines, including increased growth and maturation. These data reveal a new and previously unsuspected role for postsynaptic kainate receptors in the induction of functional and structural plasticity in the hippocampus

Blocking GABAA inhibition reveals AMPA- and NMDA-receptor-mediated polysynaptic responses in the CA1 region of the rat hippocampus

inhibition reveals AMPA- and NMDA-receptor-mediated polysyn- observations suggest that a similar activity may develop unaptic responses in the CA1 region of the rat hippocampus. J. Neu- der certain conditions. First, although less developed than rophysiol. 77: 2071–2082, 1997. We have investigated the condi- in the CA3 region, excitatory recurrent connections between tions required to evoke polysynaptic responses in the isolated CA1 pyramidal cells have been described (Deuchars and Thomregion of hippocampal slices from Wistar adult rats. Experiments were performed with extracellular and whole cell recording tech- son 1996; Thomson and Radpour 1991). Second, a-aminoniques. In the presence of bicuculline (10 mM), 6-cyano-7-nitro- 3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-quinoxaline-2-3-dione (10 mM), glycine (10 mM), and a low exand/or N-methyl-D-aspartate (NMDA)-receptor-mediated ternal concentration of Mg burst have been recorded after blockade of g-aminobutyric 2 / (0.3 mM), electrical stimulation of the Schaffer collaterals/commissural pathway evoked graded N- acid-A (GABAA) (Dingledine et al. 1986; Williamson and methyl-D-aspartate (NMDA)-receptor-mediated late field poten- Wheal 1992) or adenosine A1 receptors (in low external tials in the stratum radiatum of the CA1 region. These responses Mg 2 / conditions) (Klishin et al. 1995). However, it rewere generated via polysynaptic connections because their latency mained unclear if these events are polysynaptic and if the

Microscopic study of the Halperin–Laughlin interface through matrix product states

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