2019/05/31 by Luca F. Tocchio, Arianna Montorsi, Federico Becca · 32 citations
Materials Science · Physics and Astronomy · #Advanced Condensed Matter Physics #Charge (physics) #Condensed matter physics #Ground state #Hubbard model #Magnetic and transport properties of perovskites and related materials #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Spin (aerodynamics) #Superconductivity #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.21468/scipostphys.7.2.021
published in SciPost Physics 7(2) (SciPost.org) · 17 pages, 8 figures, submission to SciPost
arxiv created 2019/07/15 · openalex publication_date 2019/08/12 · arxiv updated 2019/08/14 · openalex created_date 2019/08/22 · openalex updated_date 2026/08/05
The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with M <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>M</mml:mi> </mml:math> legs (with M <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>M</mml:mi> </mml:math> ranging from 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>2</mml:mn> </mml:math> to 10 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>10</mml:mn> </mml:math> ) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity λ=8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> in the charge and 2λ=16 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:math> in the spin can be stabilized at doping δ=1/8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> . Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with λ=6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> , appears at δ=1/6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> . Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at δ=1/12 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mn>12</mml:mn> </mml:mrow> </mml:math> and metallic with strong superconducting correlations at δ=1/10 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> , as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.