Advanced Computing Platform for Theoretical Physics

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Commit b9f4300c by Pan Zhang

### fix an error on ln \lambda_max

parent 44c1245d
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 ... @@ -62,7 +62,8 @@ ... @@ -62,7 +62,8 @@ "### Autograd of the leading eigenvalue of the transfer matrix\n", "### Autograd of the leading eigenvalue of the transfer matrix\n", "In the last section, we have evaluated $\\ln Z$ using RG. Actually, this can be evaluated analytically as\n", "In the last section, we have evaluated $\\ln Z$ using RG. Actually, this can be evaluated analytically as\n", "$$\\ln Z =\n", "$$\\ln Z =\n", "\\frac{1}{t}\\lim_{t\\to\\infty}\\ln \\mathrm{tr}(T^t)=\\frac{1}{t}\\lim_{t\\to\\infty}\\sum_{i=1}^N \\lambda_i^t=\\lambda_\\mathrm{max},$$\n", "\\frac{1}{t}\\lim_{t\\to\\infty}\\ln \\mathrm{tr}(T^t)=\\frac{1}{t}\\lim_{t\\to\\infty}\\ln\\sum_{i=1}^N \\lambda_i^t=\n", "\\ln\\lambda_\\mathrm{max},$$\n", "where $\\lambda_{\\mathrm{max}}$ is the leading eigenvalue. Thus we can do back propagation directly on $\\lambda_{\\mathrm{max}}$." "where $\\lambda_{\\mathrm{max}}$ is the leading eigenvalue. Thus we can do back propagation directly on $\\lambda_{\\mathrm{max}}$." ] ] }, }, ... ...
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