Unified phase diagram of antiferromagnetic SU(N) spin ladders

Weichselbaum, Andreas; Capponi, S.; Lecheminant, P.; Tsvelik, A. M.; Läuchli, A. M.

doi:10.1103/PhysRevB.98.085104

Title: Unified phase diagram of antiferromagnetic SU( $N$ ) spin ladders

Abstract

Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU ( N ) spin ladders. Two-leg ladders provide a rich and highly nontrivial extension of the single chain case on the way towards the relatively little explored two-dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and 2 ≤ N ≤ 6, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, J_⊥/J_∥, strongly differ for even versus odd N. For even N = 4 and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of N/2 rungs. For odd N = 3 and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of N rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd N, albeit of a different nature for N = 3 as compared to N = 5. Formore »« less

Authors:

Weichselbaum, Andreas ^[1]; Capponi, S. ^[2]; Lecheminant, P. ^[3]; Tsvelik, A. M. ^[4]; Läuchli, A. M. ^[5]

Ludwig-Maximilians-Univ., Munich (Germany). Physics Dept., Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience; Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science
Univ. de Toulouse (France). Lab. de Physique Théorique, IRSAMC
Univ. de Cergy-Pontoise, Cergy-Pontoise (France). Site de Saint-Martin
Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Condensed Matter Physics and Materials Science
Univ. Innsbruck (Austria). Inst. fur Theoretische Physik

Publication Date:: Fri Aug 03 00:00:00 EDT 2018

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1466592

Alternate Identifier(s):: OSTI ID: 1462793

Report Number(s):: BNL-207997-2018-JAAM
Journal ID: ISSN 2469-9950; PRBMDO

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 98; Journal Issue: 8; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., and Läuchli, A. M. Unified phase diagram of antiferromagnetic SU(N) spin ladders.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevB.98.085104.

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                    Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., & Läuchli, A. M. Unified phase diagram of antiferromagnetic SU(N) spin ladders.  United States.  https://doi.org/10.1103/PhysRevB.98.085104

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                    Weichselbaum, Andreas, Capponi, S., Lecheminant, P., Tsvelik, A. M., and Läuchli, A. M. Fri .  
"Unified phase diagram of antiferromagnetic SU(N) spin ladders".  United States.  https://doi.org/10.1103/PhysRevB.98.085104.  https://www.osti.gov/servlets/purl/1466592.

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@article{osti_1466592,

  title        = {Unified phase diagram of antiferromagnetic SU(N) spin ladders},

  author       = {Weichselbaum, Andreas and Capponi, S. and Lecheminant, P. and Tsvelik, A. M. and Läuchli, A. M.},

  abstractNote = {Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU ( N ) spin ladders. Two-leg ladders provide a rich and highly nontrivial extension of the single chain case on the way towards the relatively little explored two-dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and 2 ≤ N ≤ 6, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, J⊥/J∥, strongly differ for even versus odd N. For even N = 4 and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of N/2 rungs. For odd N = 3 and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of N rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd N, albeit of a different nature for N = 3 as compared to N = 5. For N = 3, we find a novel gapless intermediate phase with J⊥-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For N = 5 , there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear. Lastly, our results are based on (i) field theoretical techniques, (ii) qualitative symmetry considerations, and (iii) large-scale density matrix renormalization group (DMRG) simulations keeping beyond a million of states by fully exploiting and thus preserving the SU (N) symmetry.},

  doi          = {10.1103/PhysRevB.98.085104},

  journal      = {Physical Review B},

  number       = 8,

  volume       = 98,

  place        = {United States},

  year         = {Fri Aug 03 00:00:00 EDT 2018},

  month        = {Fri Aug 03 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

SU(3) fermions on the honeycomb lattice at $\frac{1}{3}$ filling
journal, July 2019

Chung, Sangwoo S.; Corboz, Philippe
Physical Review B, Vol. 100, Issue 3
DOI: 10.1103/physrevb.100.035134

Dimerization and effective decoupling in two spin-1 generalizations of the spin- $\frac{1}{2}$ Majumdar-Ghosh chain
journal, September 2019

Chepiga, Natalia; Mila, Frédéric
Physical Review B, Vol. 100, Issue 10
DOI: 10.1103/physrevb.100.104426

Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders
text, January 2018

Robinson, Neil J.; Altland, Alexander; Egger, Reinhold
arXiv
DOI: 10.48550/arxiv.1806.01925

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Title: Unified phase diagram of antiferromagnetic SU( N ) spin ladders

Abstract

Citation Formats

Ultracold Fermi gases with emergent SU( N ) symmetry journal, November 2014

Identifying symmetry-protected topological order by entanglement entropy journal, December 2013

One-Dimensional Chain of Anisotropic Spin-Spin Interactions. III. Applications journal, November 1966

Fractionally Charged Excitations in Charge-Density-Wave Systems with Commensurability 3 journal, March 1981

Topological phases of spin chains journal, March 2013

Valence-bond states for quantum computation journal, December 2004

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Two-orbital S U(N) magnetism with ultracold alkaline-earth atoms journal, February 2010

Three-Sublattice Ordering of the SU(3) Heisenberg Model of Three-Flavor Fermions on the Square and Cubic Lattices journal, December 2010

Generalization of the Haldane conjecture to SU(3) chains journal, November 2017

Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice journal, May 2016

Magnetic states of the two-leg-ladder alkali metal iron selenides A Fe 2 Se 3 journal, January 2013

Site-Resolved Imaging of Fermionic Li 6 in an Optical Lattice journal, May 2015

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains journal, April 1996

Lattice of double wells for manipulating pairs of cold atoms journal, March 2006

Direct Probing of the Mott Crossover in the SU ( N ) Fermi-Hubbard Model journal, June 2016

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions journal, August 2014

Topological liquids and valence cluster states in two-dimensional SU ( N ) magnets journal, November 2011

Exact critical exponents for quantum spin chains, non-linear σ-models at θ=π and the quantum hall effect journal, March 1986

Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials journal, February 1996

Pomeranchuk Cooling of SU ( 2 N ) Ultracold Fermions in Optical Lattices journal, May 2013

Density matrix formulation for quantum renormalization groups journal, November 1992

Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism journal, August 2014

Magnetic Phase Diagram of the S =1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau journal, March 2003

SU ( N ) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations journal, October 2011

Condensation of magnons and spinons in a frustrated ladder journal, June 2006

Spin ladders and quantum simulators for Tomonaga–Luttinger liquids journal, December 2012

Metal-insulator transition in the one-dimensional SU ( N ) Hubbard model journal, July 1999

Iron displacements and magnetoelastic coupling in the antiferromagnetic spin-ladder compound BaFe 2 Se 3 journal, November 2011

Observation of a Spin Gap in Sr Cu 2 O 3 Comprising Spin-½ Quasi-1D Two-Leg Ladders journal, December 1994

Two soluble models of an antiferromagnetic chain journal, December 1961

Model for a multicomponent quantum system journal, November 1975

High-temperature properties of fermionic alkaline-earth-metal atoms in optical lattices journal, April 2012

Density matrix renormalization group simulations of SU( N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz journal, April 2018

Direct Observation of Coherent Interorbital Spin-Exchange Dynamics journal, September 2014

Two-leg SU ( 2 n ) spin ladder: A low-energy effective field theory approach journal, May 2015

Spin gap and symmetry breaking in CuO 2 layers and other antiferromagnets journal, April 1988

The density-matrix renormalization group in the age of matrix product states journal, January 2011

Entropy Dependence of Correlations in One-Dimensional SU ( N ) Antiferromagnets journal, November 2012

Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour journal, May 2000

Adiabatic Loading of One-Dimensional SU ( N ) Alkaline-Earth-Atom Fermions in Optical Lattices journal, November 2012

Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state journal, May 2013

Non-abelian symmetries in tensor networks: A quantum symmetry space approach journal, December 2012

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models journal, December 1988

Bond-operator representation of quantum spins: Mean-field theory of frustrated quantum Heisenberg antiferromagnets journal, May 1990

RG flows in the D-series of minimal CFTs journal, July 1993

Integrable perturbations of ZN parafermion models and the O(3) sigma model journal, November 1991

Spin-Orbital Quantum Liquid on the Honeycomb Lattice journal, November 2012

The scaling region of the tricritical Ising model in two dimensions journal, January 1991

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid journal, September 2009

Symmetric and asymmetric excitations of a strong-leg quantum spin ladder journal, September 2013

Massless renormalization group flow in SU ( N ) k perturbed conformal field theory journal, December 2015

Spin liquid phase of the S = 1 2 J 1 − J 2 Heisenberg model on the triangular lattice journal, July 2015

Simultaneous Dimerization and SU(4) Symmetry Breaking of 4-Color Fermions on the Square Lattice journal, November 2011

Site-resolved imaging of a fermionic Mott insulator journal, February 2016

Spinon confinement and the Haldane gap in SU ( n ) spin chains journal, November 2009

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice journal, March 2012

Probing Nearest-Neighbor Correlations of Ultracold Fermions in an Optical Lattice journal, April 2011

Quantum-Gas Microscope for Fermionic Atoms journal, May 2015

Spectral flow between conformal field theories in 1 + 1 dimensions journal, February 1992

Quantum phases of bosons in double-well optical lattices journal, October 2007

Semisynthetic zigzag optical lattice for ultracold bosons journal, December 2016

Observation of chiral currents with ultracold atoms in bosonic ladders journal, July 2014

A one-dimensional liquid of fermions with tunable spin journal, February 2014

A proof of part of Haldane's conjecture on spin chains journal, July 1986

INTEGRABLE DEFORMATIONS IN Z N -SYMMETRICAL MODELS OF THE CONFORMAL QUANTUM FIELD THEORY journal, May 1991

Frustrated three-leg spin tubes: From spin 1 ∕ 2 with chirality to spin 3 ∕ 2 journal, January 2006

Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group journal, January 1997

Spontaneous Plaquette Formation in the SU(4) Spin-Orbital Ladder journal, April 2001

Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model journal, September 2016

A Mott insulator of fermionic atoms in an optical lattice journal, September 2008

Confinement of fractional quantum number particles in a condensed-matter system journal, November 2009

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system journal, October 2009

Variational Monte Carlo investigation of SU ( N ) Heisenberg chains journal, May 2015

From tricritical Ising to critical Ising by thermodynamic Bethe ansatz journal, July 1991

Title: Unified phase diagram of antiferromagnetic SU( $N$ ) spin ladders

Ultracold Fermi gases with emergent SU( N ) symmetry
journal, November 2014

Identifying symmetry-protected topological order by entanglement entropy
journal, December 2013

One-Dimensional Chain of Anisotropic Spin-Spin Interactions. III. Applications
journal, November 1966

Fractionally Charged Excitations in Charge-Density-Wave Systems with Commensurability 3
journal, March 1981

Topological phases of spin chains
journal, March 2013

Valence-bond states for quantum computation
journal, December 2004

Entanglement entropy and conformal field theory
journal, December 2009

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods
journal, February 2018

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
journal, February 2015

Two-orbital S U(N) magnetism with ultracold alkaline-earth atoms
journal, February 2010

Three-Sublattice Ordering of the SU(3) Heisenberg Model of Three-Flavor Fermions on the Square and Cubic Lattices
journal, December 2010

Generalization of the Haldane conjecture to SU(3) chains
journal, November 2017

Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice
journal, May 2016

Magnetic states of the two-leg-ladder alkali metal iron selenides $A$ Fe $_{2}$ Se $_{3}$
journal, January 2013

Site-Resolved Imaging of Fermionic ${}^{6}{Li}$ in an Optical Lattice
journal, May 2015

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains
journal, April 1996

Lattice of double wells for manipulating pairs of cold atoms
journal, March 2006

Direct Probing of the Mott Crossover in the $SU (N)$ Fermi-Hubbard Model
journal, June 2016

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
journal, August 2014

Topological liquids and valence cluster states in two-dimensional SU $(N)$ magnets
journal, November 2011

Exact critical exponents for quantum spin chains, non-linear σ-models at θ=π and the quantum hall effect
journal, March 1986

Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
journal, February 1996

Pomeranchuk Cooling of $SU (2 N)$ Ultracold Fermions in Optical Lattices
journal, May 2013

Density matrix formulation for quantum renormalization groups
journal, November 1992

Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
journal, August 2014

Magnetic Phase Diagram of the S =1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau
journal, March 2003

SU $(N)$ magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
journal, October 2011

Condensation of magnons and spinons in a frustrated ladder
journal, June 2006

Spin ladders and quantum simulators for Tomonaga–Luttinger liquids
journal, December 2012

Metal-insulator transition in the one-dimensional $SU (N)$ Hubbard model
journal, July 1999

Iron displacements and magnetoelastic coupling in the antiferromagnetic spin-ladder compound BaFe $_{2}$ Se $_{3}$
journal, November 2011

Observation of a Spin Gap in Sr ${Cu}_{2}$ $O_{3}$ Comprising Spin-½ Quasi-1D Two-Leg Ladders
journal, December 1994

Two soluble models of an antiferromagnetic chain
journal, December 1961

Model for a multicomponent quantum system
journal, November 1975

High-temperature properties of fermionic alkaline-earth-metal atoms in optical lattices
journal, April 2012

Density matrix renormalization group simulations of SU( $N$ ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz
journal, April 2018

Direct Observation of Coherent Interorbital Spin-Exchange Dynamics
journal, September 2014

Two-leg $SU (2 n)$ spin ladder: A low-energy effective field theory approach
journal, May 2015

Spin gap and symmetry breaking in ${CuO}_{2}$ layers and other antiferromagnets
journal, April 1988

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Entropy Dependence of Correlations in One-Dimensional $SU (N)$ Antiferromagnets
journal, November 2012

Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour
journal, May 2000

Adiabatic Loading of One-Dimensional $SU (N)$ Alkaline-Earth-Atom Fermions in Optical Lattices
journal, November 2012

Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
journal, May 2013

Non-abelian symmetries in tensor networks: A quantum symmetry space approach
journal, December 2012

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models
journal, December 1988

Bond-operator representation of quantum spins: Mean-field theory of frustrated quantum Heisenberg antiferromagnets
journal, May 1990

RG flows in the D-series of minimal CFTs
journal, July 1993

Integrable perturbations of ZN parafermion models and the O(3) sigma model
journal, November 1991

Spin-Orbital Quantum Liquid on the Honeycomb Lattice
journal, November 2012

The scaling region of the tricritical Ising model in two dimensions
journal, January 1991

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
journal, September 2009

Symmetric and asymmetric excitations of a strong-leg quantum spin ladder
journal, September 2013

Massless renormalization group flow in $SU {(N)}_{k}$ perturbed conformal field theory
journal, December 2015

Spin liquid phase of the $S = \frac{1}{2} J_{1} - J_{2}$ Heisenberg model on the triangular lattice
journal, July 2015

Simultaneous Dimerization and SU(4) Symmetry Breaking of 4-Color Fermions on the Square Lattice
journal, November 2011

Site-resolved imaging of a fermionic Mott insulator
journal, February 2016

Spinon confinement and the Haldane gap in $SU (n)$ spin chains
journal, November 2009

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
journal, March 2012

Probing Nearest-Neighbor Correlations of Ultracold Fermions in an Optical Lattice
journal, April 2011

Quantum-Gas Microscope for Fermionic Atoms
journal, May 2015

Spectral flow between conformal field theories in 1 + 1 dimensions
journal, February 1992

Quantum phases of bosons in double-well optical lattices
journal, October 2007

Semisynthetic zigzag optical lattice for ultracold bosons
journal, December 2016

Observation of chiral currents with ultracold atoms in bosonic ladders
journal, July 2014

A one-dimensional liquid of fermions with tunable spin
journal, February 2014

A proof of part of Haldane's conjecture on spin chains
journal, July 1986

INTEGRABLE DEFORMATIONS IN Z _N -SYMMETRICAL MODELS OF THE CONFORMAL QUANTUM FIELD THEORY
journal, May 1991

Frustrated three-leg spin tubes: From spin $1 ∕ 2$ with chirality to spin $3 ∕ 2$
journal, January 2006

Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group
journal, January 1997

Spontaneous Plaquette Formation in the SU(4) Spin-Orbital Ladder
journal, April 2001

Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model
journal, September 2016

A Mott insulator of fermionic atoms in an optical lattice
journal, September 2008

Confinement of fractional quantum number particles in a condensed-matter system
journal, November 2009

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system
journal, October 2009

Variational Monte Carlo investigation of $SU (N)$ Heisenberg chains
journal, May 2015

From tricritical Ising to critical Ising by thermodynamic Bethe ansatz
journal, July 1991

Spontaneous trimerization in a bilinear-biquadratic $S = 1$ zig-zag chain
journal, December 2007

Spontaneous Plaquette Formation in the SU(4) Spin-Orbital Ladder
text, January 2001