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Subir Sachdev - One of the best experts on this subject based on the ideXlab platform.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global $\mathbb{Z}_N$ symmetry, to a gapped phase with the $\mathbb{Z}_N$ symmetry restored. The transition has dynamical critical exponent $z \neq 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\nu$.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_{N}$ symmetry, to a gapped phase with the ${\mathbb{Z}}_{N}$ symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single-boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\ensuremath{\nu}$.
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numerical study of the chiral z 3 quantum phase transition in one Spatial Dimension
Physical Review A, 2018Co-Authors: Rhine Samajdar, Soonwon Choi, Hannes Pichler, Mikhail D Lukin, Subir SachdevAbstract:Recent experiments on a one-Dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and Spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.
Seth Whitsitt - One of the best experts on this subject based on the ideXlab platform.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_{N}$ symmetry, to a gapped phase with the ${\mathbb{Z}}_{N}$ symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single-boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\ensuremath{\nu}$.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global $\mathbb{Z}_N$ symmetry, to a gapped phase with the $\mathbb{Z}_N$ symmetry restored. The transition has dynamical critical exponent $z \neq 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\nu$.
F W M Boekema - One of the best experts on this subject based on the ideXlab platform.
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the Spatial Dimension of social capital
European Planning Studies, 2010Co-Authors: Roel Rutten, Hans Westlund, F W M BoekemaAbstract:Social capital pertains to the social relations between humans, and since these social relations have a Spatial Dimension, so too does social capital. However, the Spatial Dimension of social capit ...
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the Spatial Dimension of social capital
Research Papers in Economics, 2009Co-Authors: Roel Rutten, Hans Westlund, F W M BoekemaAbstract:Social capital pertains to the social relations between humans, and since these social relations have a Spatial Dimension, so too does social capital. However, the Spatial Dimension of social capital has received little attention in the literature so far. Even in a globalizing world where electronic and virtual communication have the potential to defeat the need for geographical proximity, it is still relevant to consider the Spatial Dimension of social capital. After all, human beings exist most prominently in real rather than in virtual space. This special issue undertakes an inquiry into the Spatial Dimension of social capital from an explorative perspective. It aims to further theoretical and empirical understanding of the Spatial Dimension of social capital. As editors we recognize that the debate on social capital is still ongoing in the literature and that it is fed from different, sometimes conflicting perspectives. Therefore, the Spatial Dimension of social capital can only be conceptualized in the light of these different perspectives, which necessitates an explorative approach. Nonetheless, the various contributions of this special issue allow several conclusions that are valuable to the ongoing discussion on social capital and its Spatial Dimension. In the first part of this introductory paper, we discuss social capital from a conceptual angle, as we distinguish between two key approaches (the “structuralist” and “interactionist” approaches). We then argue how these approaches may be helpful to the understanding of the Spatial Dimension of social capital. In the second part, we introduce the various contributions and explain how they contribute to the aim of this special issue.
Wei Zhang - One of the best experts on this subject based on the ideXlab platform.
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huffman coding based adaptive Spatial modulation
IEEE Transactions on Wireless Communications, 2017Co-Authors: Wei Wang, Wei ZhangAbstract:Antenna switch enables multiple antennas to share a common RF chain. It also offers an additional Spatial Dimension, i.e., antenna index, that can be utilized for data transmission via both signal space and Spatial Dimension. In this paper, we propose a Huffman coding-based adaptive Spatial modulation that generalizes both conventional Spatial modulation and transmit antenna selection. Through the Huffman coding, i.e., designing variable length prefix codes, the transmit antennas can be activated with different probabilities. When the input signal is Gaussian distributed, the optimal antenna activation probability is derived through optimizing channel capacity. To make the optimization tractable, closed form upper bound and lower bound are derived as the effective approximations of channel capacity. When the input is discrete QAM signal, the optimal antenna activation probability is derived through minimizing symbol error rate. Numerical results show that the proposed adaptive transmission offers considerable performance improvement over the conventional Spatial modulation and transmit antenna selection.
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adaptive Spatial modulation using huffman coding
Global Communications Conference, 2016Co-Authors: Wei Wang, Wei ZhangAbstract:Antenna switch enables multiple antennas to share a common RF chain, thus an additional Spatial Dimension, i.e., antenna index, can be utilized in the design of single RF chain MIMO and information can be conveyed via both signal space and Spatial Dimension. In this paper, we propose a unified adaptive transmission scheme - adaptive Spatial modulation that allocates information into signal space and Spatial Dimension in order to maximize the overall channel capacity for single RF chain MIMO. The proposed adaptive Spatial modulation is realized by using Huffman coding, i.e., designing variable length codes to activate the transmit antenna with different probabilities. The optimal antenna activation probability is derived through optimizing channel capacity. To make the optimization tractable, closed form upper bound and lower bound are derived as the effective approximations for channel capacity. Numerical results show that the proposed adaptive Spatial modulation offers considerable performance improvement over both Spatial modulation and transmit antenna selection.
Rhine Samajdar - One of the best experts on this subject based on the ideXlab platform.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global $\mathbb{Z}_N$ symmetry, to a gapped phase with the $\mathbb{Z}_N$ symmetry restored. The transition has dynamical critical exponent $z \neq 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\nu$.
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quantum field theory for the chiral clock transition in one Spatial Dimension
Physical Review B, 2018Co-Authors: Rhine Samajdar, Subir Sachdev, Seth WhitsittAbstract:We describe the quantum phase transition in the $N$-state chiral clock model in Spatial Dimension $d=1$. With couplings chosen to preserve time-reversal and Spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-Dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_{N}$ symmetry, to a gapped phase with the ${\mathbb{Z}}_{N}$ symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single-boson condensate in the background of a higher-Dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\ensuremath{\nu}$.
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numerical study of the chiral z 3 quantum phase transition in one Spatial Dimension
Physical Review A, 2018Co-Authors: Rhine Samajdar, Soonwon Choi, Hannes Pichler, Mikhail D Lukin, Subir SachdevAbstract:Recent experiments on a one-Dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and Spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.
