arXiv subjects

Natalia Chepiga

Publications and source records attributed to Natalia Chepiga.

50 records · Page 3Linked to original sources

arXiv2020

Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the grand-challenge problem of the many-electron Schrodinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed matter physics and chemistry, while retaining a connection to the paradigmatic Hubbard model. Here we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition and an intricate set of intertwined magnetic orders.

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arXiv2020

Critical properties of a comb lattice

In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.

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arXiv2020

Floating, critical and dimerized phases in a frustrated spin-3/2 chain

We study spontaneous dimerization and emergent criticality in a spin-3/2 chain with antiferromagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$ and three-site $J_3$ interactions. In the absence of three-site interaction $J_3$, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of $J_2/J_1$, going successively through a critical commesurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large $J_2/J_1$. In the field theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough $J_3$, the fully dimerized phase is stabilized for all $J_2$, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)$_3$ along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2)$_3$ model. By contrast, the transition between the two dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin-1/2 edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing $J_2$ in favour of a reorganization of the dimerization pattern.

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arXiv2019

Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain

We perform a systematic DMRG investigation of the two natural spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain, the spin-1 $J_1-J_2$ Heisenberg chain, where $J_2$ is a next-nearest neighbor Heisenberg coupling, and the spin-1 $J_1-J_3$ model, where $J_3$ refers to a three-site interaction defined by $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+\mathrm {H.c.}\right]$. Although both models are rigorously equivalent to the Majumdar-Ghosh chain for spin-1/2, their physics appears to be quite different for spin 1. Indeed, when all couplings are antiferromagnetic, the spin-1 $J_1-J_2$ model undergoes an effective decoupling into two next-nearest neighbour (NNN) Haldane chains upon increasing $J_2$, while the $J_1-J_3$ chain undergoes a spontaneous dimerization similar to the spin-1/2 Majumdar-Ghosh chain upon increasing $J_3$. By extending the phase diagram to all signs of the couplings, we show that both the dimerized and the NNN-Haldane phase are actually present in the $J_1-J_3$ model, the former one adjacent to the Haldane one, the latter one to the ferromagneric one, with an Ising transition between them. By contrast, the $J_1-J_2$ chain only has a NNN-Haldane phase between the Haldane phase and the ferromagnetic phase for positive $J_2$. In both cases, our DMRG data are consistent with a continuous Kosterlitz-Thouless transition between the NNN-Haldane and the ferromagnetic phases.

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arXiv2019

Comb tensor networks

In this paper we propose a special type of a tree tensor network that has the geometry of a comb---a 1D backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher dimensional objects with special limited interactions, or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave-function as a comb tensor network, and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group (DMRG) algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge.

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arXiv2019

DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Building on the constraints imposed on the dimers, we develop a Density Matrix Renormalization Group algorithm that takes full advantage of the relatively small Hilbert space that only grows as Fibonacci number. We further show that both models can be mapped rigorously onto a hard-boson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B 69, 075106 (2004)], and combining early results with recent results obtained with the present algorithm on this hard-boson model, we discuss the full phase diagram of these quantum dimer and quantum loop models, with special emphasis on the phase transitions. In particular, using conformal field theory, we fully characterize the Ising transition and the tricritical Ising end point, with a complete analysis of the boundary-field correspondence for the tricritical Ising point including partially polarized edges. Finally, we show that the Fibonacci anyon chain is exactly equivalent to special critical points of these models.

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arXiv2018

Floating phase versus chiral transition in a 1D hard-boson model

We investigate the nature of the phase transition between the period-three charge-density wave and the disordered phase of a hard-boson model proposed in the context of cold-atom experiments. Building on a density-matrix renormalization group algorithm that takes full advantage of the hard-boson constraints, we study systems with up to 9'000 sites and calculate the correlation length and the wave-vector of the incommensurate short-range correlations with unprecedented accuracy. We provide strong numerical evidence that there is an intermediate floating phase far enough from the integrable Potts point, while in its vicinity, our numerical data are consistent with a unique transition in the Huse-Fisher chiral universality class.

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arXiv2018

Rigorous decoupling between edge states in frustrated spin chains and ladders

We investigate the occurrence of exact zero modes in one-dimensional quantum magnets of finite length that possess edge states. Building on conclusions first reached in the context of the spin-1/2 XY chain in a field, then for the spin-1 $J_1-J_2$ Heisenberg model, we show that the development of incommensurate correlations in the bulk invariably leads to oscillations in the sign of the coupling between edge states, hence to exact zero energy modes at the crossing points where the coupling between the edge states rigorously vanishes. This is true regardless of the origin of the frustration (e.g. next-nearest neighbor coupling or biquadratic coupling for the spin-1 chain), of the value of the bulk spin (we report on spin-1/2, spin-1 and spin-2 examples), and of the value of the edge-state emergent spin (spin-1/2 or spin-1).

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arXiv2017

Excitation spectrum and Density Matrix Renormalization Group iterations

We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational Matrix Product State formulation of the Density Matrix Renormalization Group (DMRG), a remarkable property since the effective Hamiltonian is only constructed to target the ground state. Conversely, modes that are very flat over several consecutive iterations are systematically found to correspond to faithful excitations. We suggest to use this property to extract accurate information about excited states using the standard ground state algorithm. The results are spectacular for critical systems, for which the low-energy conformal tower of states can be obtained very accurately at essentially no additional cost, as demonstrated by confirming the predictions of boundary conformal field theory for two simple minimal models - the transverse-field Ising model and the critical three-state Potts model. This approach is also very efficient to detect the quasi-degenerate low-energy excitations in topological phases, and to identify localized excitations in systems with impurities. Finally, using the variance of the Hamiltonian as a criterion, we assess the accuracy of the resulting Matrix Product State representations of the excited states.

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arXiv2017

Exact zero modes in frustrated Haldane chains

We show that the effective coupling between the spin-1/2 edge states of a spin-1 chain of finite length can be continuously tuned by frustration. For the $J_1-J_2$ model with nearest and next-nearest neighbor antiferromagnetic interactions, we show that the effective coupling in a chain of length $L$ changes sign $N\simeq 0.38 L$ times in the window $0.28\lesssim J_2/J_1 \lesssim 0.75$ where the short-range correlations are incommensurate. This implies that there are $N$ zero modes where the singlet and the triplet are strictly degenerate, i.e. $N$ values of $J_2/J_1$ where the spin-1/2 edge states are completely decoupled. We argue that this effect must be generic for all incommensurate phases with localized edge states, and we briefly discuss a few experimental implications.

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arXiv2016

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+{\mathrm H.c.}\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2)_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2)_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

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arXiv2016

Comment on "Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain"

The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conclusions regarding the nature of the phase transitions to the dimerized phase: i) We provide numerical evidence of a continuous Ising transition between the NNN-Haldane phase and the dimerized phase; ii) We show that the tri-critical end point, where the continuous transition between the Haldane phase and the dimerized phase turns into a first order transition, is distinct from the triple point where the three phases meet; iii) Finally, we demonstrate that the tri-critical end point is in the same Wess-Zumino-Witten (WZW) SU(2) level 2 universality class as the continuous transition line that ends at this point

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arXiv2016

Dimerization transitions in spin-1 chains

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We argue that these features are generic because of a marginal operator in the WZW SU(2)$_2$ model, and because of two topologically distinct non-dimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.

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arXiv2013

Berry phase investigation of spin-S ladders

We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of non-frustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated to a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated to a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as cross-overs between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these cross-overs turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.

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