Density matrix numerical renormalization group for non-Abelian symmetries

Tóth, A.; Moca, Cătălin Paşcu; Legeza, Örs; Zaránd, Gergely

doi:10.1103/physrevb.78.245109

Cited by 81 publications

(99 citation statements)

References 36 publications

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“…9,10 However, QCPs are challenging to reach even in engineered systems, since perturbations that steer away from quantum criticality may be inherently uncontrolled, as in two-impurity Kondo experiments to date.…”

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confidence: 99%

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Keller

Peeters

Moca

et al. 2015

Nature

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114

103

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Quantum critical systems derive their finite temperature properties from the influence of a zero temperature quantum phase transition.1 The paradigm is essential for understanding unconventional high-T c superconductors and the nonFermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated.Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behavior to distinct Fermi liquid ground states in a highly controllable quantum dot device. Our device realizes the non-Fermi liquid two-channel Kondo state, 2, 3 based on a spin-1/2 impurity exchange-coupled equally to two independent electronic reservoirs. 4 Arbitrarily small detuning of the exchange couplings results in conventional screening of the spin by the more strongly coupled channel for energies below a Fermi liquid scale T * . We extract a quadratic dependence of T * on gate voltage close to criticality and validate an asymptotically exact description of the universal crossover between strongly correlated non-Fermi liquid and Fermi liquid states. 5, 6A conventional second-order quantum phase transition (QPT) features quantum mechan- (FL) scale that vanishes at the quantum critical point (QCP); away from the QCP, a crossover from non-FL to FL behavior is observed at low energies. A diverging effective mass m * at the QCP, seen in both materials, signifies the absence of quasiparticles at the Fermi surface. 8In many heavy fermion materials and in high-T c superconductors, the relevant degrees of freedom and the effective Hamiltonian can be controversial. We aim to understand quantitatively a second-order QPT outside the usual order-parameter-fluctuation description.Quantum dots provide an experimental framework for realizing known quantum impurityHamiltonians that can feature tunable second-order QPTs. 9, 10 However, QCPs are challenging to reach even in engineered systems, since perturbations that steer away from quantum criticality may be inherently uncontrolled, as in two-impurity Kondo experiments to date. 11-13At the QCP of a two-channel Kondo (2CK) system, a single overscreened spin yields a non-FL state with no quasiparticles (i.e. only collective excitations) at the Fermi surface.An order parameter is typically not invoked; rather, the critical behavior is owing to the single spin. A FL scale T * results from several relevant perturbations: Zeeman splitting, difference in exchange couplings, and charge transfer between the two channels. Requiring that all these perturbations be small would seem to diminish prospects for observing the QCP in bulk systems. Nonetheless, two-channel Kondo physics has been invoked to explain experiments on heavy fermion materials 14-16 and two-level tunneling centers. 17-19 A 2CK state has been predicted 2 and observed 3 in a quantum dot tunnel-coupled to a "metallic grain," an electron reservoir big enough to have a small lev...

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confidence: 99%

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Keller

Peeters

Moca

et al. 2015

Nature

Self Cite

114

103

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“…By using the complete eigenbasis of the NRG Hamiltonian, we construct the thermal density matrix of the system 29,30 , which allows us to calculate various correlation functions at arbitrary temperatures. Here, to perform calculations, we use the Budapest Flexible DM-NRG code 31,32 . The main quantity in which we are interested, apart from linear conductance, is the spin polarization, which is defined as…”

Section: Model and Methodsmentioning

confidence: 99%

Perfect spin polarization in T-shaped double quantum dots due to the spin-dependent Fano effect

Wójcik

Weymann

2014

Phys. Rev. B

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We study the spin-resolved transport properties of T-shaped double quantum dots coupled to ferromagnetic leads. Using the numerical renormalization group method, we calculate the linear conductance and the spin polarization of the current for various model parameters and at different temperatures. We show that an effective exchange field due to the presence of ferromagnets results in different conditions for Fano destructive interference in each spin channel. This spin dependence of the Fano effect leads to perfect spin polarization, the sign of which can be changed by tuning the dots' levels. Large spin polarization occurs due to Coulomb correlations in the dot, which is not directly coupled to the leads, while finite correlations in the directly-coupled dot can further enhance this effect. Moreover, we complement accurate numerical results with a simple qualitative explanation based on analytical expressions for the zero-temperature conductance. The proposed device provides a prospective example of an electrically-controlled, fully spin-polarized current source, which operates without an external magnetic field.

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“…These operators are called symmetry operators and can be used to cast the Hilbert space to smaller independent subspaces [9]. Consequently, instead of solving a large matrix eigenvalue problem, the eigenvalue spectrum can be determined by solving several smaller problems.…”

Section: Symmetries To Be Exploitedmentioning

confidence: 99%

Implementation trade-offs of the density matrix renormalization group algorithm on kilo-processor architectures

Nemes

Barcza

Nagy

et al. 2013

2013 European Conference on Circuit Theory and Design (ECCTD)

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Abstract-Numerical analysis of strongly correlated quantum lattice models has a great importance in quantum physics. The exponentially growing size of the Hilbert space makes these computations difficult, however sophisticated algorithms have been developed to balance the size of the effective Hilbert space and the accuracy of the simulation. One of these methods is the density matrix renormalization group (DMRG) algorithm which has become the leading numerical tool in the study of low dimensional lattice problems of current interest. In the algorithm a high computational problem can be translated to a list of dense matrix operations, which makes it an ideal application to fully utilize the computing power residing in both current multi-core processors and novel kilo-processor architectures.

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Density matrix numerical renormalization group for non-Abelian symmetries

Cited by 81 publications

References 36 publications

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Perfect spin polarization in T-shaped double quantum dots due to the spin-dependent Fano effect

Implementation trade-offs of the density matrix renormalization group algorithm on kilo-processor architectures

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